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CTET Paper II (Mathematics and Science) 20 Dec 2021 Solved Paper

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Question : 34 of 150

Marks: +1, -0

\sqrt[3]{8^{4}}\times \sqrt[3]{125^{2}}\div \sqrt{4^{3}}

is equal to

50
40
100
80

Solution:

Concept:

Use the law of exponents:

\sqrt[n]{a^m} = a^{m/n}

to rewrite radicals as powers.

Explanation:

Convert each term to exponent form.

\sqrt[3]{8^4} = 8^{4/3}

,

\sqrt[3]{125^2} = 125^{2/3}

, and

\sqrt{4^3} = 4^{3/2}

.

Write the bases as prime powers:

8 = 2^3

,

125 = 5^3

,

4 = 2^2

.

So the expression is

(2^3)^{4/3} \times (5^3)^{2/3} \div (2^2)^{3/2}

.

Simplify exponents:

2^{3 \times 4/3} = 2^4

,

5^{3 \times 2/3} = 5^2

,

2^{2 \times 3/2} = 2^3

.

Now compute:

2^4 \times 5^2 \div 2^3 = 16 \times 25 \div 8

.

16 \times 25 = 400

, then

400 \div 8 = 50

.

Answer:

50

(Option A).

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