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# Simplifying a product of a radical expression?

square root of 3xw^3 by the square root of 15x^5w^4. Can I get some help?

### 6 Answers

- 1 decade agoFavorite Answer
when multiplying add the numerals together

so

45

then add the exponents

(45x^6w^7)^1/2

then pull out the doubles

6x^3w^3(w)^1/2

- ireadlotsLv 61 decade ago
The site below has a good description of exponent rules.

Remember :

1) Multiplying powers with the same base, add the exponents

2) Raising powers to a new power - multiply the exponents.

3) (ab)^x = a^x * b^x

4) Square root of x = x^(1/2)

So

(3xw^3)^(1/2) * (15x^5w^4)^(1/2)

= 3^(1/2) * x^(1/2) * w^(3/2) * 3^(1/2) * 5^(1/2) * x^(5/2) * w^(4/2)

= 3^(1/2 + 1/2) * 5^(1/2) * x^(1/2 + 5/2) * w^(3/2 + 4/2)

= 3√5 x^3*w^(7/2)

= 3√5x^3√(w^7)

- DOVELv 61 decade ago
square root of 3xw^3 by the square root of 15x^5w^4.

=square root of (3xw^3 by 15x^5w^4.)

=square root of (3xw^3/15x^5w^4.)

=sqrt( 3/15 x/x^5 w^3/w^4)

sqrt( 1/5 1/x^4 1/ w)

= 1/x^2 sqrt (1/ 5w)

- TomVLv 71 decade ago
sqrt(3xw^3)*sqrt(15x^5w^4) = sqrt((3xw^3)(15x^5w^4))

= sqrt(45x^6w^7) = 3x^3sqrt(5w^7) = 3sqrt(5)(x^3)w^(7/2)

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- fenimoreLv 44 years ago
in accordance to the surds and indices, the manufactured from capacity of a variable with capacity is likewise elevated i.e. (x^a)^b = x^ab So, given (x^3)^3/4 = (x)^3*3/4 = x^9/4 for this reason, (x^3)^3/4 = x^9/4 desire it helps u lot!

- 1 decade ago
Can you explain the question a little more? I'm not sure exactly what you're trying to do