Find the value of 4{147} - 4/3 {1/3} - {1/27}

Correct Answer is : 24739{247{3}}{9}92473

Correct Answer is : 24739{247{3}}{9}92473

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AFCAT I 23 Jan 2025 Shift 2 Paper

Question : 81 of 100

Marks: +1, -0

4\sqrt{147} - \frac{4}{3} \sqrt{\frac{1}{3}} - \sqrt{\frac{1}{27}}

Solution:

The given expression may be written as:

\; \Rightarrow 4 \sqrt{147} - \frac{4}{3} \sqrt{\frac{1}{3}} - \sqrt{\frac{1}{27}}

\; = 4 \sqrt{9 \times \frac{49}{3}} - \frac{4}{3} \sqrt{\frac{1}{3}} - \sqrt{\frac{1}{3 \times 3 \times 3}}

\; = \frac{84}{\sqrt{3}} - \frac{4}{3\sqrt{3}} - \frac{1}{3\sqrt{3}}

\; = \frac{252-4-1}{3\sqrt{3}}

Multiplying

\sqrt{3}

in numerator and denominator

\; = \frac{247}{3\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}

\; = \frac{247\sqrt{3}}{9}

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