# Surds and Indices Quiz Set 008

### Question 1

What is \$({5/23})^0.05 × ({5/23})^x = ({5/23})^3.2\$?

A

3.15.

B

3.65.

C

4.65.

D

5.15.

Soln.
Ans: a

We can simplify the given expression to \$({5/23})^{0.05 + x} = ({5/23})^3.2\$. The bases are equal, so the powers should also be equal. Hence \$0.05 + x = 3.2\$ which gives x = 3.15.

### Question 2

If \$√65\$ is approximately \$8\$, then what is \$65^3.5\$?

A

2097152.

B

2097153.

C

2097151.

D

2097154.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$65^3.5\$ is same as \$(√65)^7\$ which gives \$8^7\$ = 2097152.

### Question 3

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.

### Question 4

If \$√47\$ is approximately \$6\$, then what is \$47^2\$?

A

1296.

B

1297.

C

1295.

D

1298.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$47^2\$ is same as \$(√47)^4\$ which gives \$6^4\$ = 1296.

### Question 5

If \$4^{m + n} = 16384\$, and \$4^{m - n} = 256\$, then what is m?

A

5.5.

B

6.0.

C

7.0.

D

8.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$4^{m + n} = 4^7\$ and \$4^{m - n} = 4^4\$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations \$m + n = 7\$ and \$m - n = 4\$. Solving, we get \$m = {7 + 4}/2\$ = 5.5. Note: The trick in such type of questions is to keep an eye on the "bases".