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3 years ago

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

Mathematics

1 answer:

liubo4ka [24]3 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

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Find the surface area of a cylinder with the following dimensions. Use 3. 14 for $. Round your answer to the nearest

kupik [55]

Answer:

Step-by-step explanation:

r=d/2=11.4/2=5.7

slant surface area=2πr*h=11.4×3.14×4.4=157.5024 cm^2

area of base and top=2(πr²)=2×3.14×(5.7)²=204.0372 cm²

total surface area=157.5024+204.0372=361.5396=361.5 sq. cm

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2 years ago

A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take

Lina20 [59]

Answer:

The 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion <em>P</em> is:

$CI=p\pm z_{\alpha/2}\sqrt{\frac{p(1- p)}{n}}$

The information provided is:

<em>x</em> = number of students who responded as"yes" = 70

<em>n</em> = sample size = 200

Confidence level = 95%

The formula to compute the sample proportion is:

$p=\frac{x}{n}$

The R codes for the construction of the 95% confidence interval is:

> x=70

> n=200

> p=x/n

> p

[1] 0.35

> s=sqrt((p*(1-p))/n)

> s

[1] 0.03372684

> E=qnorm(0.975)*s

> lower=p-E

> upper=p+E

> lower

[1] 0.2838966

> upper

[1] 0.4161034

Thus, the 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

7 0

2 years ago

Read 2 more answers

PLLLLSSS HELP ME ASAP!

erastovalidia [21]

The answer to the first one is ' D '.
(All the angles inside a triangle have to add up to exactly 180 degrees.)

The answer to the second one is ' C ' .
(If two sides are equal, then the sides opposite them are also equal.)

3 0

2 years ago

A restaurant offers diet soda and regular soda.In one day they sold 64 sodas.If 28 of the sodas they sold were diet, what is the

german

Answer: The ratio of regular sodas sold to diet sodas sold is 9:7

Step-by-step explanation:

The restaurant offers diet soda and regular soda.

In one day they sold a total of 64 sodas. If 28 of the sodas they sold were diet sodas, the rest would be regular sodas. Therefore, the number of regular sodas sold will be 64 - 28 = 36 regular sodas. The ratio of regular sodas sold to diet sodas sold would be the number of regular sodas sold divided by the number of diet sodas sold. It becomes

36/28 = 18/14 = 9/7

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2 years ago

Kelsey can buy 2 pounds of apples for 7$. Write an equation to represent the cost, c, for a, pounds of apples.

zmey [24]

$\huge\boxed{c=3.5a}$