Math help Please?

Question

Evalutate

square root of 4/25 ?

Also this one has me stumped

sqrt63 - 2sqrt28 + 5sqrt7

THanks

Answer 1

1) 0.4
2) 10.583

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Let's walk through the solution....
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The first question is design to demonstrate the rule
sqrt (x/y) = sqrt(x) / sqrt(y)

So sqrt(4/15) = sqrt(2*2)/sqrt(5*5) = 2/5 = 0.4

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The second question illustrates the rules

sqrt(x*y) = sqrt(x)*sqrt(y)

a*sqrt(x)+b*sqrt(x) = (a+b)*sqrt(x)


So....
sqrt63 - 2sqrt28 + 5sqrt7 =
sqrt(3*3*7) - 2*sqrt(2*2*7) + 5*sqrt(7) =
sqrt(3*3)*sqrt(7) - 2*2*sqrt(7) + 5*sqrt(7) =
3*sqrt(7) - 4*sqrt(7) + 5*sqrt(7)

To make it clearer... we're going to pretend x = sqrt(7)

3x-4x+5x = 4x

Subsituting x back with sqrt(7), you get
4*sqrt(7) = 10.583....

Answer 2

1) 2/5
2) 4 * 7^½

For a square root of a fraction, take the square root of the top and bottom separately, then perform any reducing required or "rationalizing" to not have square roots in the divisor. So 4/25 would yield 2 and 5 so 2/5.

For the second one, break the numbers the square roots are being taken of into factors and look for factors which are perfect squares. The square root of a number is the square roots of the various factors times each other. So the square root of 63 is the square root of 9 times the square root of 7, the square root of 28 is the square root of 4 times the square root of 7, and the square root of 7 is, well, the square root of 7. If you use this fact and resolve the square roots of the perfect squares you find, the problem looks like this: 63^½ - 2 * 28^½ + 5 * 7^½ = 9^½ * 7^½ - 2 * 4^½ * 7^½ + 5 * 7^½ = 3 * 7^½ - 4 * 7^½ + 5 * 7^½. Now, if you factor that, factoring out the 7^½ you get 7^½ * (3 - 4 + 5) and that equals: 4 * 7^½. Which happens to be about as reduced as one can make it so...

Answer 3

make them into radicals. well 21 and 3 equal 63 so you put 21 and 3 under the sqrt sign. then since 21 can be broken down into 7 and 3 you multiply radical 3 and radical 3 to get 3 then you get 3 sqrt 7. 2 sqrt of 28 you do the same thing. 7 and 4 equal 28. so you put both numbers under a sqrt sign. sqrt of 4 is 2 so you multiply it by the 2 in front and get 4 sqrt 7. last one you leave alone and if you put 3sqrt7-4sqrt7 +5 sqrt7 you get? 4 sqrt 7!!!!

Answer 4

Square root of 4/25 is 0.4

Answer 5

square root of 4/25
= sqrt(4)/sqrt(25)
= 2/5 = 4/10 = 0.4

sqrt63 - 2sqrt28 + 5sqrt7
= sqrt(9 *7) - 2sqrt(4*7) + 5sqrt(7)
= sqrt(9)*sqrt(7) - 2*sqrt(4)*sqrt(7) + 5sqrt(7)
=3sqrt(7) -4sqrt(7) +5sqrt(7)
= 4sqrt(7)

Answer 6

2/5

For the other, try reducing the numbers under the square to multiples of sqrt 7. Then you'll be able to add and subtract them.

Answer 7

0.4 i think for sqrt 4/25

Answer 8

√(4/25)=√(2^2/5^2)=2/5

√63-2√28+5√7
√(3^2*7)-2√(2^2*7)+5√7
3√7-4√7+5√7=4√7

Answer 9

sq rt 4/sq rt 25=2/5

sr7*sr9-2(sr7*sr4)+5sr7
=3sr7-4sr7+5sr7
=4sr7

Answer 10

0.4 for the first one. 10.58 for the second one