Simplify - 4 - 3 - 2 - 345

Here, we need to simplify the inner most radicals first. x4 #160;x3 #160;x2x345=x4 #160;x3 #160;x2 #215;x12345=x4 #160;x3 #160;x2+12345=x4 #160; ...

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Byju's Answer

Standard IX

Mathematics

BODMAS

Simplify × 4 ...

Question

Simplify $\sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \sqrt{x}}}} .$

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Solution

Here, we need to simplify the inner most radicals first.
$\sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \sqrt{x}}}} = \sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \times x^{\frac{1}{2}}}}} = \sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2 + \frac{1}{2}}}}} = \sqrt[5]{x^{4} \sqrt[4]{x^{3} \times x^{\frac{5}{2 \times 3}}}} = \sqrt[5]{x^{4} \sqrt[4]{x^{3 + \frac{5}{6}}}} = \sqrt[5]{x^{4} \sqrt[4]{x^{\frac{23}{6}}}} = \sqrt[5]{x^{4} \times x^{\frac{23}{24}}} = \sqrt[5]{x^{4 + \frac{23}{24}}} = \sqrt[5]{x^{\frac{119}{24}}} = x^{\frac{119}{24 \times 5}} = x^{\frac{119}{120}}$
Hence, $\sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \sqrt{x}}}} = x^{\frac{119}{120}}$ .

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Similar questions

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(i) $3 \sqrt{45} - \sqrt{125} + \sqrt{200} - \sqrt{50}$
(ii) $2 \frac{\sqrt{30}}{\sqrt{6}} - 3 \frac{\sqrt{140}}{\sqrt{28}} + \frac{\sqrt{55}}{\sqrt{99}}$
(iii) $\sqrt{72} + \sqrt{800} - \sqrt{18}$

Q. Simplify :

\sqrt{2} \times \sqrt[3]{3} \times \sqrt[4]{4}

Q. Simplify :

[3]^{4} \times [(3)^{2}]^{4}

Q. Simplify:

\frac{4 \sqrt{3}}{2 - \sqrt{2}} - \frac{30}{4 \sqrt{3} - 3 \sqrt{2}} - \frac{3 \sqrt{2}}{3 + 2 \sqrt{3}}

Q. Simplify 4

\frac{3}{4}

- 2

\frac{1}{2}

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Simplify x4 x3 x2x345.

Here, we need to simplify the inner most radicals first. x4 x3 x2x345=x4 x3 x2×x12345=x4 x3 x2+12345=x4 x3 ×x52×345=x4 x3+5645=x4 x23645=x4 ×x23245=x4+23245=x119245=x11924×5=x119120 Hence, x4 x3 x2x345=x119120.

Simplify $\sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \sqrt{x}}}} .$