Question

Evaluate under root 0.9 up to 3 decimal places
Step by step

Answer 1

Answer:

0.949

Step-by-step explanation:

Evaluate under √0.9 up to 3 decimal places

First we will simplify the 0.9 by removing decimal

0.9 = $\frac{9}{10}$

$\sqrt{0.9} = \sqrt{\frac{9}{10}}$

Lets multiply the numerator & Denominator by 10 to make the denominator as whole square.

$\sqrt{0.9} = \sqrt{\frac{9\times10}{10\times10}} \\\\\sqrt{0.9} = \sqrt{\frac{3\times3\times10}{10\times10}} \\\\\sqrt{0.9} = \frac{3}{10} \times \sqrt{10}$

Putting values of √10 = 3.162

$\sqrt{0.9} = \frac{3}{10} \times 3.162\\\\\sqrt{0.9} = \frac{3}{10} \times 3.162\\\\\sqrt{0.9} = \frac{9.486}{10}\\\\\sqrt{0.9} = 0.9486\\\\\sqrt{0.9} = 0.949$

Answer 2

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$\huge{\blue{\boxed{\orange{\boxed{\mathcal{\purple{HELLO}}}}}}}$

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$\huge\star\underline\mathtt\purple{Answer:-}$

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$\huge\mathtt{≈ \: 0.949}$

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$\huge\star\underline\mathtt\purple{Explanation-}$

$\huge\mathtt { = > 0.9 = \frac{9}{10} }$

$\huge\mathtt {we \: can \: write \: it } \\ \\ \huge\mathtt { as \: =}$

$\huge\mathtt{ \sqrt{0.9} = \sqrt{ \frac{9 \times 10}{10 \times 10} } }$

$\huge\mathtt{= \sqrt{0.9}} \\ \\ \huge\mathtt{ \: \: \: \: \: \: \: \: = \frac{3}{10} \times \sqrt{10} }$

$\huge\mathtt{as \: \sqrt{10}} \\ \huge\mathtt{= 3.162} \\ \\ \: \: \: \: \: \huge\mathtt{ \sqrt{0.9} = \frac{3}{10} \times \frac{3162}{1000} }$

$\huge\mathtt{ = \sqrt{0.9}} \\ \\ \huge\mathtt{ = \frac{9.486}{10} } \\ \\ \huge\mathtt{ \sqrt{0.9} = 0.9486} \\ \\ \huge\mathtt{ \sqrt{0.9} \: ≈ \: 0.9490} \\ \\ \huge\mathtt{ \sqrt{0.9} \: = 0.949}$

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