Simplify the following surds- -75 - -108 - -192-

The given surds can be simplified as follows: √( 75 ) +√( 108 ) √( 192 ) =√( 25× 3 ) +√( 36× 3 ) √( 64× 3 ) =5√( 3 ) +6√( 3 ) 8√( 3 ) =√( 3 ) (5+6 8)=3√( ...

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Byju's Answer

Standard IX

Mathematics

Addition and Subtraction of Surds

Simplify the ...

Question

Simplify the following surds:
$\sqrt{75} + \sqrt{108} - \sqrt{192}$ .

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Solution

The given surds can be simplified as follows:
$\sqrt{75} + \sqrt{108} - \sqrt{192} = \sqrt{25 \times 3} + \sqrt{36 \times 3} - \sqrt{64 \times 3} = 5 \sqrt{3} + 6 \sqrt{3} - 8 \sqrt{3} = \sqrt{3} (5 + 6 - 8) = 3 \sqrt{3}$

Hence, $\sqrt{75} + \sqrt{108} - \sqrt{192} = 3 \sqrt{3}$ ..

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Similar questions

Q. Classify the following into like surds:

\sqrt[3]{24}, \sqrt[3]{81}, \sqrt[3]{108}, \sqrt[3]{192}, \sqrt[3]{2916}

Q. Simplify

\sqrt{27} + \sqrt{48} - \sqrt{12} + \sqrt{75} - \sqrt{108}

Q. Simplify the following surds.

(i)

\sqrt{27}

(ii)

\sqrt{50}

(iii)

\sqrt{250}

(iv)

\sqrt{112}

(v)

\sqrt{168}

Q. Simplify :

\frac{4}{7} \sqrt{147} + \frac{3}{8} \sqrt{192} - \frac{1}{5} \sqrt{75}

Q. Divide and simplify:

\frac{12 \sqrt{75}}{4 \sqrt{108}}

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Simplify the following surds:√75+√108−√192.

The given surds can be simplified as follows:√75+√108−√192=√25×3+√36×3−√64×3=5√3+6√3−8√3=√3(5+6−8)=3√3Hence, √75+√108−√192=3√3..

Simplify the following surds:
$\sqrt{75} + \sqrt{108} - \sqrt{192}$ .

The given surds can be simplified as follows:
$\sqrt{75} + \sqrt{108} - \sqrt{192} = \sqrt{25 \times 3} + \sqrt{36 \times 3} - \sqrt{64 \times 3} = 5 \sqrt{3} + 6 \sqrt{3} - 8 \sqrt{3} = \sqrt{3} (5 + 6 - 8) = 3 \sqrt{3}$

Hence, $\sqrt{75} + \sqrt{108} - \sqrt{192} = 3 \sqrt{3}$ ..