Surds and Indices Quiz Set 009

Question 1

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.

Question 2

What is \${7^499}/{7^496}\$?

A

343.

B

344.

C

342.

D

345.

Soln.
Ans: a

Simplifying, we get \$7^{499 - 496}\$ which equals\$7^3\$, or 343.

Question 3

What is \$14^1.2 × 14^x = 14^1.4\$?

A

0.2.

B

0.7.

C

1.7.

D

2.2.

Soln.
Ans: a

We can simplify the given expression to \$14^{1.2 + x} = 14^1.4\$. The bases are equal, so the powers should also be equal. Hence \$1.2 + x = 1.4\$ which gives x = 0.2.

Question 4

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 5

What is the value of x if \$(25)^1.5 × 5^9\$ ÷ \$625^3\$ = \$5^x\$?

A

0.

B

2.

C

4.

D

6.

Soln.
Ans: a

Simplifying, we get \$(5^2)^1.5 × 5^9\$ ÷ \$(5 ^ 4)^3\$ = \$5^x\$, which simplifies to \$5^3 × 5^9\$ ÷ \$5^12\$ = \$5^x.\$ Equating the powers x = 3 + 9 - 12 = 0.