# Surds and Indices Quiz Set 013

### Question 1

If \$4^{m + n} = 4096\$, and \$4^{m - n} = 64\$, then what is m?

A

4.5.

B

5.0.

C

6.0.

D

7.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$4^{m + n} = 4^6\$ and \$4^{m - n} = 4^3\$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations \$m + n = 6\$ and \$m - n = 3\$. Solving, we get \$m = {6 + 3}/2\$ = 4.5. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 2

What is \$31^3.1 × 31^x = 31^1.8\$?

A

-1.3.

B

-0.8.

C

0.2.

D

0.7.

Soln.
Ans: a

We can simplify the given expression to \$31^{3.1 + x} = 31^1.8\$. The bases are equal, so the powers should also be equal. Hence \$3.1 + x = 1.8\$ which gives x = -1.3.

### Question 3

If \$√7744 = 88\$, then what is the value of \$√77.44\$ + \$√0.7744\$ + \$√0.007744\$ + \$√0.00007744\$?

A

9.7768.

B

10.2768.

C

11.2768.

D

10.7768.

Soln.
Ans: a

We can see that \$√77.44\$ = 8.8, \$√0.7744\$ = 0.88, \$√0.007744\$ = 0.088, \$√0.00007744\$ = 0.0088. Adding, we get 9.7768 as the answer.

### Question 4

If \$√4761 = 69\$, then what is the value of \$√47.61\$ + \$√0.4761\$ + \$√0.004761\$ + \$√0.00004761\$?

A

7.6659.

B

8.1659.

C

9.1659.

D

8.6659.

Soln.
Ans: a

We can see that \$√47.61\$ = 6.9, \$√0.4761\$ = 0.69, \$√0.004761\$ = 0.069, \$√0.00004761\$ = 0.0069. Adding, we get 7.6659 as the answer.

### Question 5

If \$p^q = 512\$, then what could be \$(p - 1)^(q + 1)\$?

A

2401.

B

2402.

C

2400.

D

2403.

Soln.
Ans: a

By inspection we can see that p = 8, q= 3. So \$(8 - 1)^(3 + 1)\$ will be \$7^4\$, i.e., 2401.