Square root help... please!♥?

Question

1.) Square root (3xy) Squareroot (27xy^3)



2.) Square root (90 a^5 b^7) Divided by Square Root (10 a^3 b^4




3.) 25 Root (x ^15)


Not sure how to do each of those.. If you could help me.. that would be great. Thanks♥♥

Answer 1

1) The product of square roots is the same as the square root of the products, i.e.:

sqrt(a) * sqrt(b) = sqrt(ab)

So, remembering that multiplying adds exponents:

sqrt(3xy) * sqrt(27xy^3) =
sqrt(3xy * 27xy^3) =
sqrt(81 x^2 y^4)

And using the converse, and remembering that square root of an even exponent just divides the exponent by two:

sqrt(81 x^2 y^4) =
sqrt(81) * sqrt(x^2) * sqrt(y^4) =
9 * x * y^2 =
9xy^2

2) Same thing works for quotients.

sqrt(a) / sqrt(b) = sqrt(a / b)

So, also remembering that dividing subtracts exponents:

sqrt(90 a^5 b^7) / sqrt(10 a^3 b^4) =
sqrt( 90 a^5 b^7 / 10 a^3 b^4 ) =
sqrt( 9 a^2 b^3 ) =
sqrt(9) * sqrt(a^2) * sqrt(b^3) =
3 * a * b * sqrt(b) =
3ab * sqrt(b)

3) Not sure what you mean by "25 root x^15"?

If you mean the 25th root, then you'd just divide the exponent by 25. The 25th root of x^15 is:

x^(15/25) = x^(3/5)

You could write x^(3/5) or the fifth root of x^3, whichever is appropriate for the given assignment.

If it instead means 25 times the square root of x^15, it's:

25 sqrt(x^15) =
25 sqrt(x^14 * x) =
25 sqrt(x^14) * sqrt(x) =
25 * x^7 * sqrt(x) =
25x^7 * sqrt(x)

Answer 2

You have to combine the numbers under the squareroots

Squareroot(a)*squareroot(b) =squareroot(ab)

Squareroot(a)/squareroot(b) = squareroot(a/b)

1
Square root (3xy) Squareroot (27xy^3)
Squareroot(3xy*27xy^3)
squraeroot(81x^2*y^4)
take the squareroot of each of these terms (81, x^2, y^4 )
9xy^2

2
Square root (90 a^5 b^7) Divided by Square Root (10 a^3 b^4
squareroot( (90 a^5 b^7)/(10 a^3 b^4) )
squareroot(9a^2*b^3)
Take the squareroot of each of these terms
Because b^3 is not a perfect square, squareroot(b^3) can be expressed as squareroot(b^2*b) = b*squareroot(b)
squareroot(9a^2*b^3) = 3ab*squareroot(b)

3
25 Root (x ^15)
25x^7*squareroot(x)

Answer 3

sqrt (3xy) * sqrt ( 27 xy ^3)
=sqrt (3xy * 27 xy ^3)
= sqrt ( 3 * 27 * x ^2 * y ^4)
= sqrt { 3 * (3 * 3 * 3) * x^2 * y ^4 }
=sqrt ( 3 ^ 4 * x ^2 * y ^ 4)
= sqrt { (3 ^2) ^ 2 * x ^2 * (y ^2) ^2 }
= 3^2 * x ^2 * y ^2
= 9x ^2 y^2

{sqrt ( 90 a^5 b^ 7)} / {sqrt(10a^3b^4)}
= [sqrt {90 a^3 * a ^2 b^3 * (b^2)^2}] / [sqrt { 10 a ^2 * a (b^2)^2 }]
= (90 ^ 1/2 a ^ 3/2 a b ^ 3/2 b^2 ) / (10 ^1/2 a * a ^1/2 b ^2)
{= 9.486 a ^ (3/2 + 1) * b ^ (3/2 + 2)} / {3.162 a ^ (1 + 1/2) b^2}
= {9.486 a^5/2 b ^ 7/2 } / { 3.162 a ^ 3/2 b^2}
= (9.486/3.162) * a ^ (5/2 - 3/2 ) b^ (7/2 - 2)
= 3 * a b ^3

25 sqrt (x ^15)
= 25 x ^ 15 * 1/2
=25 x^15/2
= 25 x^ 7 1/2
= 25 x ^ 7 * x ^ 1/2
= 25 x ^ 7 * sqrt (x)

Answer 4

1. Square root of 27 is square root of 9 and 3.
9 is the square root of 3.
3 square root of 3 is the answer for 27. xy to the third is the square root of xy^3 because there is no whole number square root. The square root sign remains.
2. 90 a^5 b^7
9 and 10 . Do your square roots and 3 sq root of 10 equals 90. a and b remain 5 and 7 because there is no whole number square root.
When you divide subtract the a to the third with the a to the fifth.
Your answer is : 3a^2b^3
3. 5 and x square root of 15.

Answer 5

squareroot(3xy)squareroot(27xy^3)
= squareroot(3xy*27xy^3)
since squareroot(a)squareroot(b)= squareroot(ab)
=squareroot(81x^2y^4)
=81^.5 * (x^2)^.5 * (y^4)^.5
= 9 x y^2
=9xy^2

Square root (90 a^5 b^7) / Square Root (10 a^3 b^4)
=Square root (90 a^5 b^7/(10 a^3 b^4))
since squareroot(a)/squareroot(b)= squareroot(a/b)
=Square root (9 a^2 b^3)
=3ab*Squareroot(b)

25 Root (x ^15)
if this is the 25th root of x^15, that is like saying (x^15)^(1/25)
since the nth root of p is p^(1/n)
= x^(15/25) = x^(2/3) of the cube root of x^2
since (x^a)^b = x^(ab)

if this is 25 time the square root of x^15, then is it like saying 25(x^15)^.5 = 25(x^(15*.5)) = 25x^(7.5) = 25x^7 * squareroot(x)

Hope that helps, good luck!

Answer 6

1) I assume you mean to multiply these. You get the sqrt of the product, 81 x^2 y^4

Now the sqrt is 9 x y^2

2) sqrt 9 a^2 b^3 which is 3 a b sqrt b

3) 25 sqrt x^14 times sqrt x = 25 x^7 sqrt x

Answer 7

sqrt(3xy)sqrt(27xy3)=9xy^2
write 27 as 3root3 and take ysquare out of root.

2. it wud be equal to root(90/10*a5/a3*b7/b4)
taking 9a2b2 out of the root, b is left behind.
hence,
3ab*root(b)

3. take x14 out
= 25x7*rootx