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Vikentia [17]
2 years ago
5

Simplify. Assume that all variables represent positive real numbers. sqrt[45][x]^[7][y]^[8]

Mathematics
2 answers:
Lisa [10]2 years ago
4 0

Answer:

3 x^3 y^4 sqrt(5x)

Step-by-step explanation:

sqrt(45x^7y^8)

We know that sqrt(ab) = sqrt(a)sqrt(b)

sqrt(45)sqrt(x^7) sqrt(y^8)

sqrt(9*5) sqrt(x^2 *x^2 * x^2* x) sqrt(y^2 *y^2 *y^2 *y^2)

We know that sqrt(ab) = sqrt(a)sqrt(b)

sqrt(9)sqrt(5) sqrt(x^2)sqrt(x^2) sqrt(x^2) sqrt(x) sqrt(y^2)sqrt(y^2)sqrt(y^2)sqrt(y^2)

3 sqrt(5) x*x*x sqrt(x) y*y*y*y

3 x^3 y^4 sqrt(5)sqrt(x)

3 x^3 y^4 sqrt(5x)

AVprozaik [17]2 years ago
3 0

Answer:

3 x^3 * y^4*√(5x)

Step-by-step explanation:

Factor

45: <u>3 * 3</u> * 5

y^8 = <u>y * y</u> * <u>y * y</u> *<u>y * y</u> * <u>y * y</u>

x^7 = <u>x *x</u> *<u>x *x </u>*<u>x *x</u> *x

Now underline every pair.

Rule: for every pair, take 1 outside the square root sign and throw the other one away. If any of the bases are left over, leave them under the square root sign.

3 * y * y * y * y * x * x * x *  √ (5 * y)

Answer: 3 x^3 * y^4*√(5x)

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