# Surds and Indices Quiz Set 011

### Question 1

What is the value of x if \$(625)^1.5 × 5^5\$ ÷ \$25^2.5\$ = \$5^x\$?

A

6.

B

10.

C

14.

D

18.

Soln.
Ans: a

Simplifying, we get \$(5^4)^1.5 × 5^5\$ ÷ \$(5 ^ 2)^2.5\$ = \$5^x\$, which simplifies to \$5^6 × 5^5\$ ÷ \$5^5\$ = \$5^x.\$ Equating the powers x = 6 + 5 - 5 = 6.

### Question 2

If \$8^{m + n} = 2097152\$, and \$8^{m - n} = 4096\$, 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 \$8^{m + n} = 8^7\$ and \$8^{m - n} = 8^4\$. 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".

### Question 3

If \$p^q = 36\$, then what could be \$(p - 1)^(q + 1)\$?

A

125.

B

126.

C

124.

D

127.

Soln.
Ans: a

By inspection we can see that p = 6, q= 2. So \$(6 - 1)^(2 + 1)\$ will be \$5^3\$, i.e., 125.

### Question 4

If \$√54\$ is approximately \$7\$, then what is \$54^1.5\$?

A

343.

B

344.

C

342.

D

345.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$54^1.5\$ is same as \$(√54)^3\$ which gives \$7^3\$ = 343.

### Question 5

If \$√5329 = 73\$, then what is the value of \$√53.29\$ + \$√0.5329\$ + \$√0.005329\$ + \$√0.00005329\$?

A

8.1103.

B

8.6103.

C

9.6103.

D

9.1103.

Soln.
Ans: a

We can see that \$√53.29\$ = 7.3, \$√0.5329\$ = 0.73, \$√0.005329\$ = 0.073, \$√0.00005329\$ = 0.0073. Adding, we get 8.1103 as the answer.