15-10-20-40-5-80is being given that -5-2-236 and -10-3-162

√(20)=√(4× 5)=2√(5) √(40)=√(4× 10)=2√(10) √(80)=√(16× 5)=4√(5) So, 15/√(10)+√(20)+√(40)+√(5) √(80) =15/√(10)+2√(5)+2√(10) √(5) 4√(5) =15/3√(10) 3√(5)×3√(10)+ ...

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Byju's Answer

Standard IX

Mathematics

Expansion of (a ± b ± c)²

15/√10+√20+√4...

Question

$\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} + \sqrt{5} - \sqrt{80}}$
is being given that $\sqrt{5} = 2.236 a n d \sqrt{10} = 3.162$

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Solution

$\sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5}$
$\sqrt{40} = \sqrt{4 \times 10} = 2 \sqrt{10} \sqrt{80} = \sqrt{16 \times 5} = 4 \sqrt{5} S o, \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} + \sqrt{5} - \sqrt{80}} = \frac{15}{\sqrt{10} + 2 \sqrt{5} + 2 \sqrt{10} - \sqrt{5} - 4 \sqrt{5}} = \frac{15}{3 \sqrt{10} - 3 \sqrt{5}} \times \frac{3 \sqrt{10} + 3 \sqrt{5}}{3 \sqrt{10} + 3 \sqrt{5}} = \frac{45 \sqrt{10} + 45 \sqrt{5}}{(3 \sqrt{10})^{2} - (3 \sqrt{5})^{2}} = \frac{45 (3 \sqrt{10} + 3 \sqrt{5})}{90 - 45} = \frac{4 / 5 (\sqrt{10}) + \sqrt{5}}{4 / 5} = \sqrt{10} + \sqrt{5} = 3.162 + 2.236 = 5.398$

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Similar questions

Q. Evaluate

\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}

, it being given that

\sqrt{5} = 2.236

and

\sqrt{10} = 3.162

Evaluate $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$ , it us given that $\sqrt{5} = 2.236$ and $\sqrt{10} = 3.162$

Q. Evaluate

\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}

, it being given that

\sqrt{5} = 2.236 and \sqrt{10} = 3.162

.
Hint

\begin{array}{rcl} \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} & = & \frac{15}{\sqrt{10} + 2 \sqrt{5} + 2 \sqrt{10} - \sqrt{5} - 4 \sqrt{5}} \\ = & \frac{15}{3 \sqrt{10} - 3 \sqrt{5}} = \frac{5}{\sqrt{10} - \sqrt{5}} \end{array}

Q. Evaluate after rationalising the denominator of 25/(√40 - √80) , it being given that √5 = 2.236 and √10 = 3.162

Q. If

\sqrt{5} = 2.236

and

\sqrt{10} = 3.162, t h e v a l u e o f \frac{\sqrt{10} - \sqrt{5}}{\sqrt{2}}

on simplifying is

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15√10+√20+√40+√5−√80 is being given that √5=2.236and√10=3.162

√20=√4×5=2√5 √40=√4×10=2√10√80=√16×5=4√5So,15√10+√20+√40+√5−√80=15√10+2√5+2√10−√5−4√5=153√10−3√5×3√10+3√53√10+3√5=45√10+45√5(3√10)2−(3√5)2=45(3√10+3√5)90−45=4/5(√10)+√54/5=√10+√5=3.162+2.236=5.398

$\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} + \sqrt{5} - \sqrt{80}}$
is being given that $\sqrt{5} = 2.236 a n d \sqrt{10} = 3.162$