Given that $\sqrt{3} = 1.7321$ , find the correct value to 3 places of decimal of the following.
$\sqrt{192} - \frac{1}{2} \sqrt{48} - \sqrt{75}$

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Solution

$\sqrt{192} - \frac{1}{2} \sqrt{48} - \sqrt{75}$
$= \sqrt{64 \times 3} - \frac{1}{2} \sqrt{16 \times 3} - \sqrt{25 \times 3}$
$= \sqrt{64} \sqrt{3} - \frac{1}{2} 4 \sqrt{3} - \sqrt{25} \sqrt{25}$
$= 8 \sqrt{3} - \frac{1}{2} 4 \sqrt{3} - 5 \sqrt{3}$
$= 8 \sqrt{3} - 2 \sqrt{3} - 5 \sqrt{3}$
$= 1.732$

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Similar questions

Q. Given that

\sqrt{3} = 1.7321

, find the value of

100

times the given expression

\sqrt{192} - \frac{1}{2} \sqrt{48} - \sqrt{75}

Given, $\sqrt{2} = 1.4141 a n d \sqrt{6} = 2.449, f i n d t h e v a l u e o f \frac{1}{\sqrt{3} - \sqrt{2} - 1}$ correct to 3 places of decimal.

Q. Given that

\sqrt{3} = 1.732

, then the value of

\sqrt{75} + \frac{1}{2} \sqrt{48} - \sqrt{192}

= - 1.732

Find the values of each of the following correct to three places of decimals, it being given that $\sqrt{2} = 1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4492 a n d \sqrt{10} = 3.162$ .

(i) $\frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}}$

(ii) $\frac{1 + \sqrt{2}}{3 - 2 \sqrt{2}}$

Find the value of $3 \sqrt{48} - 4 \sqrt{75} + 5 \sqrt{192}$

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Given that √3=1.7321, find the correct value to 3 places of decimal of the following.√192−12√48−√75

√192−12√48−√75=√64×3−12√16×3−√25×3=√64√3−124√3−√25√25=8√3−124√3−5√3=8√3−2√3−5√3=1.732

Given that $\sqrt{3} = 1.7321$ , find the correct value to 3 places of decimal of the following.
$\sqrt{192} - \frac{1}{2} \sqrt{48} - \sqrt{75}$

$\sqrt{192} - \frac{1}{2} \sqrt{48} - \sqrt{75}$
$= \sqrt{64 \times 3} - \frac{1}{2} \sqrt{16 \times 3} - \sqrt{25 \times 3}$
$= \sqrt{64} \sqrt{3} - \frac{1}{2} 4 \sqrt{3} - \sqrt{25} \sqrt{25}$
$= 8 \sqrt{3} - \frac{1}{2} 4 \sqrt{3} - 5 \sqrt{3}$
$= 8 \sqrt{3} - 2 \sqrt{3} - 5 \sqrt{3}$
$= 1.732$