# Surds and Indices Quiz Set 005

### Question 1

If \$2^{m + n} = 32\$, and \$2^{m - n} = 4\$, then what is m?

A

3.5.

B

4.0.

C

5.0.

D

6.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$2^{m + n} = 2^5\$ and \$2^{m - n} = 2^2\$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations \$m + n = 5\$ and \$m - n = 2\$. Solving, we get \$m = {5 + 2}/2\$ = 3.5. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 2

What is \${4^584}/{4^581}\$?

A

64.

B

65.

C

63.

D

66.

Soln.
Ans: a

Simplifying, we get \$4^{584 - 581}\$ which equals\$4^3\$, or 64.

### Question 3

If \$√4489 = 67\$, then what is the value of \$√44.89\$ + \$√0.4489\$ + \$√0.004489\$ + \$√0.00004489\$?

A

7.4437.

B

7.9437.

C

8.9437.

D

8.4437.

Soln.
Ans: a

We can see that \$√44.89\$ = 6.7, \$√0.4489\$ = 0.67, \$√0.004489\$ = 0.067, \$√0.00004489\$ = 0.0067. Adding, we get 7.4437 as the answer.

### Question 4

What is the value of x if \$(64)^3 × 2^3\$ ÷ \$16^1.5\$ = \$2^x\$?

A

15.

B

21.

C

27.

D

33.

Soln.
Ans: a

Simplifying, we get \$(2^6)^3 × 2^3\$ ÷ \$(2 ^ 4)^1.5\$ = \$2^x\$, which simplifies to \$2^18 × 2^3\$ ÷ \$2^6\$ = \$2^x.\$ Equating the powers x = 18 + 3 - 6 = 15.

### Question 5

If \$13^1.1 = p, and 13^2.5 = q\$ and \$p^m = q^4\$ then what is the value of m?

A

9.09.

B

9.33.

C

9.23.

D

9.63.

Soln.
Ans: a

Substituting in \$p^m = q^4\$, we get \$13^{1.1m} = 13^{2.5 × 4}\$. Bases are same so powers should be same. Hence, \$1.1m = {2.5 × 4}\$, which gives m = 9.09. 