Question

$\sf \huge\fbox {\underline{Question}}$


find the square root 576 by using
(prime factorization method)

also show of LCM/HCF calculation

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Answer 1

Step-by-step explanation:

Solution

we know that , 576 is a perfect square

$\bf \: 576 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$

If we'll take the square root of both the left and right hand sides, we get

$\bf \sqrt{576} = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$

Now,

$\bf \sqrt{576}= 2 \times 2 \times 3 \times 3 \\ \bf \sqrt{576} = 24 \\ \\ \bf \: Hence, \: the \: square \: root \: of \: 576 \: is \: 24.$

Hope it'll help you :-D

have a nice day

Answer 2

Answer:

tex] \sf \huge\fbox {\underline{Question}}[/tex]

find the square root 576 by using

(prime factorization method)

also show of LCM/HCF calculation

$\huge \dag \sf \red{Answer}$

${\huge{\underline{\small{\mathbb{\pink{REFER \ TO \ THE \ ATTACHMENT}}}}}}$

$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$

Total number of 2 is 6 and total number of 3 is 2

We'll write it in exponential form

${2}^{6} \times {3}^{2}$

$\implies \: \sqrt{576} \\ \\ = \sqrt{ {2}^{6} \times {3}^{2} }$

Divide the exponent

=6÷2=3

$= {2}^{3} \times 3 \\ \\ = 8 \times 3 = 24$

Hence 24 is the answer

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Verification:-

$\sqrt{574} \\ \\ = \sqrt{24 \times 24} \\ \\ = 24$

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Additional information:-

• Prime factorization method is a method in which the numbers are expressed as a product of their prime factors. The identical prime factors are paired and the product of one element from each pair gives the square root of the number. This method can also be used to find whether a number is a perfect square or not. However, this method cannot be used to find the square root of decimal numbers which are not perfect squares.
• The square root of a square of any number is the number itself.
• The square root of non-perfect square numbers cannot be determined using the prime factorization method. However, one can determine the number to be multiplied or divided by the given number to make it a perfect square.

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Hope it helps you from my side

:)