How do you extract square roots in scientific notation?

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How do you extract square roots in scientific notation?

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Answer 1 · 2016-04-02T05:48:47

See process and examples below.

Explanation:

In scientific notation numbers are written in the form $x \times 10^{n}$ $x xx10^n$ , where $n$ $n$ is an integer and $x$ $x$ is in limits $[1, 10)$ $[1,10)$ i.e. $1 \leq x < 10$ $1<=x<10$ .

Examples $: -$ $:-$

$53246.6$ $53246.6$ is written as $5.32466 \times 10^{4}$ $5.32466xx10^4$
$46870000$ $46870000$ is written as $4.687 \times 10^{7}$ $4.687xx10^7$
$0.0007925$ $0.0007925$ is written as $7.925 \times 10^{- 4}$ $7.925xx10^-4$
$0.0000213$ $0.0000213$ is writen as $2.13 \times 10^{- 5}$ $2.13xx10^-5$

To extract square root of such numbers

(a) if n is even just take the square root of $x$ $x$ and $10^{n}$ $10^n$ and multiply them; and

(b) if $n$ $n$ is odd, mutiply $x$ $x$ by $10$ $10$ and reduce $n$ $n$ by $1$ $1$ to make it even and then take square root of each and multiply them.

Hence

$\sqrt{5.32466 \times 10^{4}} = \sqrt{5.32466} \times \sqrt{10^{4}} = 2.3075 \times 10^{2}$ $sqrt(5.32466xx10^4)=sqrt5.32466xxsqrt(10^4)=2.3075xx10^2$
$\sqrt{4.687 \times 10^{7}} = \sqrt{46.87} \times \sqrt{10^{6}} = 6.846 \times 10^{3}$ $sqrt(4.687xx10^7)=sqrt46.87xxsqrt(10^6)=6.846xx10^3$
$\sqrt{7.925 \times 10^{- 4}} = \sqrt{7.925} \times \sqrt{10^{- 4}} = 2.815 \times 10^{- 2}$ $sqrt(7.925xx10^-4)=sqrt(7.925)xxsqrt(10^(-4))=2.815xx10^-2$
$\sqrt{2.13 \times 10^{- 5}} = \sqrt{21.3} \times \sqrt{10^{- 6}} = 4.625 \times 10^{- 3}$ $sqrt(2.13xx10^-5)=sqrt21.3xxsqrt(10^(-6))=4.625xx10^-3$

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How do you extract square roots in scientific notation?

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