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Simplifications Questions
1. Can you find the value for the expression:
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
SHOW ANSWER
Correct Ans:12.7
Explanation:
Given expression is:
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8^2)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8)]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^{4.2 + 4.2} × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^8.4 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8 * 7)^8.4 × (56)^4.3 = (56)^?
=> (56)^8.4 × (56)^4.3 = (56)^?
=> (56)^{8.4 + 4.3} = (56)^?
=> (56)^{12.7} = (56)^?
Thus the answer is : "12.7"
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8^2)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8)]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^{4.2 + 4.2} × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^8.4 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8 * 7)^8.4 × (56)^4.3 = (56)^?
=> (56)^8.4 × (56)^4.3 = (56)^?
=> (56)^{8.4 + 4.3} = (56)^?
=> (56)^{12.7} = (56)^?
Thus the answer is : "12.7"
2. Can you find the value for the expression:
6 (1/3) + 4 (1/5) + 1 (3/7) – 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
6 (1/3) + 4 (1/5) + 1 (3/7) – 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
SHOW ANSWER
Correct Ans:24 (17/35)
Explanation:
Given expression is:
6 (1/3) + 4 (1/5) + 1 (3/7) - 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
= (19 / 3) + (21 / 5) + (10 / 7) - (15 / 7) + (22 / 5) * (10 / 3)
= (19 / 3) + (21 / 5) + [(10 - 15) / 7] + (44 / 3)
= (19 / 3) + (21 / 5) - (5 / 7) + (44 / 3)
= (19 + 44) / 3 + (21 / 5) - (5 / 7)
= (63 / 3) + (21 / 5) - (5 / 7)
= 21 + (21 / 5) - (5 / 7)
On taking L.C.M we get,
= (735 + 147 - 25) / 35
= 857 / 35
= 24 (17/ 35)
6 (1/3) + 4 (1/5) + 1 (3/7) - 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
= (19 / 3) + (21 / 5) + (10 / 7) - (15 / 7) + (22 / 5) * (10 / 3)
= (19 / 3) + (21 / 5) + [(10 - 15) / 7] + (44 / 3)
= (19 / 3) + (21 / 5) - (5 / 7) + (44 / 3)
= (19 + 44) / 3 + (21 / 5) - (5 / 7)
= (63 / 3) + (21 / 5) - (5 / 7)
= 21 + (21 / 5) - (5 / 7)
On taking L.C.M we get,
= (735 + 147 - 25) / 35
= 857 / 35
= 24 (17/ 35)
3. Can you find the value for the expression:
(∛12167) × (∛274625) × (∛250047) = ?
(∛12167) × (∛274625) × (∛250047) = ?
SHOW ANSWER
Correct Ans:94185
Explanation:
Given expression is:
(∛12167) × (∛274625) × (∛250047)=?
= (∛12167) × (∛274625) × (∛250047)
= 23 × 65 × 63
= 94185
(∛12167) × (∛274625) × (∛250047)=?
= (∛12167) × (∛274625) × (∛250047)
= 23 × 65 × 63
= 94185
4. Can you find the value for the expression:
15×(1/4) + 32×(1/3) + 12×(3/4) × 7 × (1/17) = ? + 13×(1/4)
15×(1/4) + 32×(1/3) + 12×(3/4) × 7 × (1/17) = ? + 13×(1/4)
SHOW ANSWER
Correct Ans:124 x (1/3)
Explanation:
Given expression is:
15×(1/4) + 32×(1/3) + 12×(3/4) × 7×(1/17) = ? + 13×(1/4)
=> (61 / 4) + (97 / 3) + (51 / 4) * (120 / 17) = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 - (53 / 4) = ?
=> [(61 - 53) / 4] + (97 / 3) + 90 = ?
=> [8 / 4] + (97 / 3) + 90 = ?
=> 2 + (97 / 3) + 90 = ?
On taking L.C.M for left hand side, we get
=> (6 + 97 + 270) / 3 = ?
=> (373 / 3) = ?
=> 124 (1 / 3) = ?
Hence the answer is : "124 (1 / 3)"
15×(1/4) + 32×(1/3) + 12×(3/4) × 7×(1/17) = ? + 13×(1/4)
=> (61 / 4) + (97 / 3) + (51 / 4) * (120 / 17) = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 - (53 / 4) = ?
=> [(61 - 53) / 4] + (97 / 3) + 90 = ?
=> [8 / 4] + (97 / 3) + 90 = ?
=> 2 + (97 / 3) + 90 = ?
On taking L.C.M for left hand side, we get
=> (6 + 97 + 270) / 3 = ?
=> (373 / 3) = ?
=> 124 (1 / 3) = ?
Hence the answer is : "124 (1 / 3)"
5. Can you find the value for the expression:
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
SHOW ANSWER
Correct Ans:1833
Explanation:
Given expression is:
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
= (143^2 – 142^2) + (188^2 – 186^2) + ( 201^2 – 199^2)
Using Formula: a^2 – b^2 = (a+b)(a-b), we have:
(143 + 142)(143 – 142) + (188 + 186)(188 – 186) + (201 + 199)(201 – 199)
= [285 x 1] + [374 x 2] + [400 x 2]
= 285 + 748 + 800
= 1833
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
= (143^2 – 142^2) + (188^2 – 186^2) + ( 201^2 – 199^2)
Using Formula: a^2 – b^2 = (a+b)(a-b), we have:
(143 + 142)(143 – 142) + (188 + 186)(188 – 186) + (201 + 199)(201 – 199)
= [285 x 1] + [374 x 2] + [400 x 2]
= 285 + 748 + 800
= 1833
6. Can you find the value for the expression:
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
SHOW ANSWER
Correct Ans:250
Explanation:
Given expression is
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
= (1225 / 5) + (625 / 125)
= 245 + 5
= 250
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
= (1225 / 5) + (625 / 125)
= 245 + 5
= 250
7. Can you find the value for 'X' in the below expression:
[ {(144^ 2) / 48} * X] / 22 = 216
[ {(144^ 2) / 48} * X] / 22 = 216
SHOW ANSWER
Correct Ans:11
Explanation:
Given expression is
[ {(144^ 2) / 48} * X] / 22 = 216
=> [(20736 / 48) * X] / 22 = 216
=> [432 * X] / 22 = 216
=> 432 * X = 216 * 22
=> 432 * X = 4752
= X = 4752 / 432
=> X = 11
[ {(144^ 2) / 48} * X] / 22 = 216
=> [(20736 / 48) * X] / 22 = 216
=> [432 * X] / 22 = 216
=> 432 * X = 216 * 22
=> 432 * X = 4752
= X = 4752 / 432
=> X = 11
8. Can you find the value for the expression:
(9 / 13) of 221 + 1 (4 / 9) of 378 = 241 + ?
(9 / 13) of 221 + 1 (4 / 9) of 378 = 241 + ?
SHOW ANSWER
Correct Ans:458
Explanation:
Given expression is
( 9 / 13) of 221 + 1 ( 4 / 9 ) of 378 = 241 + ?
=> ( 9 / 13 ) * 221 + ( 13 / 9 ) * 378 - 241 = ?
= ( 9 * 17) + ( 13 * 42 ) - 241
= 153 + 546 - 241
= 699 - 241
= 458
( 9 / 13) of 221 + 1 ( 4 / 9 ) of 378 = 241 + ?
=> ( 9 / 13 ) * 221 + ( 13 / 9 ) * 378 - 241 = ?
= ( 9 * 17) + ( 13 * 42 ) - 241
= 153 + 546 - 241
= 699 - 241
= 458
9. Can you find the value for the expression:
5 + 55 + 555+ 5555 + 55555
5 + 55 + 555+ 5555 + 55555
SHOW ANSWER
Correct Ans:61725
Explanation:
Given expression is
5 + 55 + 555+ 5555 + 55555
By adding each and every number together we get,
= 60 + 555 + 5555 + 55555
= 615 + 5555 + 55555
= 6170 + 55555
= 61725
5 + 55 + 555+ 5555 + 55555
By adding each and every number together we get,
= 60 + 555 + 5555 + 55555
= 615 + 5555 + 55555
= 6170 + 55555
= 61725
10. Evaluate the expression: 12 / 4 + 12 / 3 + 20 - 24 / 4 + 1
SHOW ANSWER
Correct Ans:22
Explanation:
11. Èvaluate the expression: 2 + 6 - 18 / 4 + 21 - 10 / 4 - 2
SHOW ANSWER
Correct Ans:20
Explanation:
12. Evaluate the expression: 3 + 4 / 8 - 2 + 21 / 7 +7
SHOW ANSWER
Correct Ans:11.5
Explanation:
13. Evaluate the expression: 4 * 3 + 4 - 4 / 8 * 2 + 3
SHOW ANSWER
Correct Ans:18
Explanation:
Given Question:4 * 3 + 4 - 4 / 8 * 2 + 3
when we apply BODMAS RULE to the above question, we get
=> 4 * 3 + 4 - (4 / 8) * 2 + 3
= (4 * 3) + 4 - (0.5 * 2) + 3
= 12 + 4 – 1+ 3
= 19 – 1
= 18
when we apply BODMAS RULE to the above question, we get
=> 4 * 3 + 4 - (4 / 8) * 2 + 3
= (4 * 3) + 4 - (0.5 * 2) + 3
= 12 + 4 – 1+ 3
= 19 – 1
= 18
14. Evaluate the expression: 1 + 2 - 30 / 4 * 6 + 13 - 12 / 3 + 3
SHOW ANSWER
Correct Ans:-30
Explanation:
15. Evalluate the expression : 22 / 4 + 12 / 3 + 20 - 24 / 6 + 13
SHOW ANSWER
Correct Ans:38.5
Explanation:
16. Evaluate the expression: 2 * 6 + 18 / 4 - 21 + 20 / 4 + 3.
SHOW ANSWER
Correct Ans:3.5
Explanation:
Given,2 * 6 + 18 / 4 - 21 + 20 / 4 + 3
when we apply BODMAS RULE to the above question, we get
=> 2 * 6 + (18 / 4) - 21 + (20 / 4) + 3
=> [2 * 6] + (4.5) - 21 + (5) + 3
=> 12 + 4.5 - 21 + 5 + 3
=> 3.5
when we apply BODMAS RULE to the above question, we get
=> 2 * 6 + (18 / 4) - 21 + (20 / 4) + 3
=> [2 * 6] + (4.5) - 21 + (5) + 3
=> 12 + 4.5 - 21 + 5 + 3
=> 3.5
17. Evaluate the expression : 3 + 6 - 10 / 4 + 3 * 2 - 2
SHOW ANSWER
Correct Ans:10.5
Explanation:
18. Evaluate the expression : 2 * 3 + 4 - 10 + 12 / 4 - 2
SHOW ANSWER
Correct Ans:1
Explanation:
19. Evaluate the expression : 1 / 2 + 3 / 4 * 2 + 3 - 6 + 12
SHOW ANSWER
Correct Ans:11
Explanation:
20. Evaluate the expression: 7 - 2 + 20 / 8 + 8 / 3 * 3
SHOW ANSWER
Correct Ans:15.5
Explanation:
Given Question is 7 - 2 + 20 / 8 + 8 / 3 * 3
when we apply BODMAS RULE to the above question, we get
=> 7 - 2 + (20 / 8) + (8 / 3) * 3
= 7 - 2 + 2.5 + (2.67 * 3)
= 7 - 2 + 2.5 + 8.01
= 17.51 – 2
= 15.51
when we apply BODMAS RULE to the above question, we get
=> 7 - 2 + (20 / 8) + (8 / 3) * 3
= 7 - 2 + 2.5 + (2.67 * 3)
= 7 - 2 + 2.5 + 8.01
= 17.51 – 2
= 15.51
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