# Surds and Indices Quiz Set 002

### Question 1

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".

### Question 2

What is \$({11/26})^0.03 × ({11/26})^x = ({11/26})^0.14\$?

A

0.11.

B

0.61.

C

1.61.

D

2.11.

Soln.
Ans: a

We can simplify the given expression to \$({11/26})^{0.03 + x} = ({11/26})^0.14\$. The bases are equal, so the powers should also be equal. Hence \$0.03 + x = 0.14\$ which gives x = 0.11.

### 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

What is \$({16/7})^2.9 × ({16/7})^x = ({16/7})^1.6\$?

A

-1.3.

B

-0.8.

C

0.2.

D

0.7.

Soln.
Ans: a

We can simplify the given expression to \$({16/7})^{2.9 + x} = ({16/7})^1.6\$. The bases are equal, so the powers should also be equal. Hence \$2.9 + x = 1.6\$ which gives x = -1.3.

### Question 5

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.