If -2-1-414- -3-1-732- -5-2-236- -10-3-162 then find the values of the -40-20 correct to 3 places of decimals-

√(40) √(20) =√(4×10) √(4×5) =2√(10) 2√(5) =2(√(10) √(5)) =2(3.162 2.236) =2(0.926) =1.852 ∴√(40) √(20) =1.852 ...

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Byju's Answer

Standard IX

Mathematics

Addition and Subtraction of Numbers with Square Root

If √2=1.414, ...

Question

If $\sqrt{2} = 1.414,$ $\sqrt{3} = 1.732,$ $\sqrt{5} = 2.236,$ $\sqrt{10} = 3.162$ then find the values of the $\sqrt{40} - \sqrt{20}$ correct to 3 places of decimals.

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Solution

$\sqrt{40} - \sqrt{20}$
$= \sqrt{4 \times 10} - \sqrt{4 \times 5}$
$= 2 \sqrt{10} - 2 \sqrt{5}$
$= 2 (\sqrt{10} - \sqrt{5})$
$= 2 (3.162 - 2.236)$
$= 2 (0.926)$
$= 1.852$
$∴ \sqrt{40} - \sqrt{20}$ $= 1.852$

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Similar questions

Find the value to three places of decimals of each of the following. It is given that $\sqrt{2} = 1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236$ and $\sqrt{10} = 3.162$ .

(i) $\frac{2}{\sqrt{3}}$

(ii) $\frac{3}{\sqrt{10}}$

(iii) $\frac{\sqrt{5} + 1}{\sqrt{2}}$

(iv) $\frac{\sqrt{10} + \sqrt{15}}{\sqrt{2}}$

(v) $\frac{2 + \sqrt{3}}{3}$

(vi) $\frac{\sqrt{2} - 1}{\sqrt{5}}$

Q. If √2 = 1.414,√3=1.732, √5=2.236 and √10=3.162, then find the value to three places of decimals in equation √10-√5/√2.

Q. Find the value to three places of decimals of each of the following. It is given that

\sqrt{2} = 1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236

and

\sqrt{10} = 3.162

(i i) \frac{3}{\sqrt{10}}

Q. Find the value to three places of decimals of each of the following. It is given that

\sqrt{2} = 1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236

and

\sqrt{10} = 3.162

\frac{3}{\sqrt{10}}

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If √2=1.414, √3=1.732, √5=2.236, √10=3.162 then find the values of the √40−√20 correct to 3 places of decimals.

√40−√20 =√4×10−√4×5 =2√10−2√5 =2(√10−√5) =2(3.162−2.236) =2(0.926) =1.852 ∴√40−√20 =1.852

If $\sqrt{2} = 1.414,$ $\sqrt{3} = 1.732,$ $\sqrt{5} = 2.236,$ $\sqrt{10} = 3.162$ then find the values of the $\sqrt{40} - \sqrt{20}$ correct to 3 places of decimals.

$\sqrt{40} - \sqrt{20}$
$= \sqrt{4 \times 10} - \sqrt{4 \times 5}$
$= 2 \sqrt{10} - 2 \sqrt{5}$
$= 2 (\sqrt{10} - \sqrt{5})$
$= 2 (3.162 - 2.236)$
$= 2 (0.926)$
$= 1.852$
$∴ \sqrt{40} - \sqrt{20}$ $= 1.852$