z o asked in Science & MathematicsMathematics · 1 decade ago

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

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  • 1 decade ago
    Favorite 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

  • 1 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)

  • DOVE
    Lv 6
    1 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)

  • TomV
    Lv 7
    1 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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  • 4 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

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