Surds and Indices Quiz Set 003

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Question 1

If $√73$ is approximately $8$, then what is $73^3$?

 A

262144.

 B

262145.

 C

262143.

 D

262146.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $73^3$ is same as $(√73)^6$ which gives $8^6$ = 262144.


Question 2

What is $({4/34})^{x - 0.18} × ({4/34})^x = ({4/34})^0.23$?

 A

0.205.

 B

0.705.

 C

1.705.

 D

2.205.

Soln.
Ans: a

We can simplify the given expression to $({4/34})^{2x - 0.18} = ({4/34})^0.23$. The bases are equal, so the powers should also be equal. Hence $2x - 0.18 = 0.23$ which gives x = 0.205.


Question 3

If $26^0.05 = p, and 26^0.34 = q$ and $p^m = q^4$ then what is the value of m?

 A

27.20.

 B

27.44.

 C

27.34.

 D

27.74.

Soln.
Ans: a

Substituting in $p^m = q^4$, we get $26^{0.05m} = 26^{0.34 × 4}$. Bases are same so powers should be same. Hence, $0.05m = {0.34 × 4}$, which gives m = 27.20.


Question 4

What is x if $7^x = 343$?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

We can write the given expression as $7^x = 7^3$. The bases are same so powers should be same. Comparing we get x = 3.


Question 5

What is ${4^513}/{4^511}$?

 A

16.

 B

17.

 C

15.

 D

18.

Soln.
Ans: a

Simplifying, we get $4^{513 - 511}$ which equals$4^2$, or 16.


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This Blog Post/Article "Surds and Indices Quiz Set 003" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-24.

Posted by Parveen(Hoven),
Aptitude Trainer


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