# Surds and Indices Quiz Set 003

### 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.