All categories

4 years ago

Can someone explain me how to find square root by prime factorization ?

Mathematics

1 answer:

liubo4ka [24]4 years ago

5 0

Answer:

<h2><u>STEPS</u></h2>

Step I: Obtain the given number.
Step II: Resolve the given number into prime factors by successive division.
Step III: Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
Step IV: Take one factor from each pair.
Step V: Find the product of factors obtained in step IV.
Step VI: The product obtained in step V is the required square root.

<h2><u>Example </u></h2>

<u> Find the square root of 324</u>

324 = 2 x 162
= 2 x 2 x 81
= 2 x 2 x 3 x 27
= 2 x 2 x 3 x 3 x 9
= 2 x 2 x 3 x 3 x 3 x 3
∴ √324 = √( 2 x 2 x 3 x 3 x 3 x 3 )
√324 = 2 x 3 x 3
√324 = 18

You might be interested in

Is 2/3 greater than 10/18

SVEN [57.7K]

2/3 is greater than 10/18

4 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%5Clarge%7B%5Cbold%20%5Cred%7B%20%5Csum%20%5Climits_%7B8%7D%5E%7B4%7D%20%7Bx%7D%5E%7B2%7D%2

kiruha [24]

Answer:

No solution

Step-by-step explanation:

We have

$\sum_{x=8}^{4}x^2 + 9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

For the sum it is not correct to assume

$\sum_{x=8}^{4}x^2= 8^2 + 7^2+6^2+5^2+4^2 = 64+49+36+25+16 = 190$

Note that for

$\sum_{x=a}^b f(x)$

it is assumed $a\leq x \leq b$ and in your case $\nexists x\in\mathbb{Z}: a\leq x\leq b$ for $a>b$

In fact, considering a set $S$ we have

$\sum_{x=a}^b (S \cup \varnothing) = \sum_{x=a}^b S + \sum_{x=a}^b \varnothing$ that satisfy $S = S \cup \varnothing$

This means that, by definition $\sum_{x=a}^b \varnothing = 0$

Therefore,

$\sum_{x=8}^{4}x^2 = 0$

because the sum is empty.

For

$9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

we have other problems. Actually, this case is really bad.

Note that $\cos^2(\infty)$ has no value. In fact, if we consider for the case

$\lim_{x \to \infty} \cos^2(x)$ , the cosine function oscillates between $[-1, 1]$ , and therefore it is undefined. Thus, we cannot evaluate

$9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

and then

$\sum_{x=8}^{4}x^2 + 9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

has no solution

7 0

3 years ago

A news service conducted a survey of 1026 adults ages 18 years or older in a certain country, August 31minus−September 2, 2015

Alex787 [66]

Ddcvv was a great night for you guys I love ya too

7 0

3 years ago

Select the correct values in the table.

s344n2d4d5 [400]

So if it can vary by 75 or less, the least it can be is 1,125 and the greatest it can be is 1275.
Therefore it must be between or equal to these two.

The answers are:
1,125
And
1,260

3 0

3 years ago

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it

Ainat [17]

<u>Answer-</u>

<em>$23377</em><em> must be deposited to get $68000 at the end of 30 years.</em>

<u>Solution-</u>

We know that for compound interest,

$A=P(1+\dfrac{r}{n})^{nt}$