Radical 54x^9y^7 simplified

Step by Step Solution

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Simplify :

sqrt(54x9y7)

STEP

1

:

Simplify the Integer part of the SQRT

Factor 54 into its prime factors

54 = 2 • 33

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

9 = 32

Factors which will remain inside the root are :

6 = 2 • 3

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

3 = 3

At the end of this step the partly simplified SQRT looks like this:

3 • sqrt (6x9y7)

STEP

2

:

Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

(1) variables with no exponent stay inside the radical

(2) variables raised to power 1 or (-1) stay inside the radical

(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

(3.1) sqrt(x8)=x4

(3.2) sqrt(x-6)=x-3

(4) variables raised to an odd exponent which is >2 or <(-2) , examples:

(4.1) sqrt(x5)=x2•sqrt(x)

(4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(x9y7) = x4y3 • SQRT(xy)

Combine both simplifications

sqrt (54x9y7) =

3 x4y3 • sqrt(6xy)

Simplified Root :

3 x4y3 • sqrt(6xy)

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

hdjd

step-by-step explanation: