SIMPLIFY.

ROOT OF 500

SIMPLIFY.ASSUME ALL VARIABLES REPRESENT POSITIVE NUMBERS.
ROOT OF X^4Y^3

DECIDE WHETHER ROOT OF 49/100 IS RATIONAL OR IRRATIONAL

500= 100*5

sqrt x^a y^b is x^(a/2) y^(b/2)

what is the square root of 7, of 100? are they rational?

22x2y14-22x4y13

To simplify the expression, "ROOT OF 500," you need to find the prime factors of 500 and look for pairs of identical factors.

First, let's find the prime factors of 500:
500 = 2 * 2 * 5 * 5 * 5

Now, let's look for pairs of identical factors:
500 = 2^2 * 5^3

Taking the square root of each factor:
√(2^2 * 5^3) = 2 * 5 * √5

So, the simplified expression for the square root of 500 is 10√5.

Now, let's simplify the expression "ROOT OF X^4Y^3":

Using the rule that √(a * b) = √a * √b, you can split the square root of a product into the square roots of individual factors:

√(X^4Y^3) = √X^4 * √Y^3

Since √X^4 = (X^4)^(1/2) = X^2 and √Y^3 = (Y^3)^(1/2) = Y^1.5, the simplified expression is:

X^2 * Y^1.5

Now, let's decide whether the square root of 49/100 is rational or irrational:

To determine if a square root is rational or irrational, we need to simplify the expression further.

√(49/100) = √49 / √100 = 7/10

The expression simplifies to the rational number 7/10. Therefore, the square root of 49/100 is rational.

As for the square root of 7 and 100, let's calculate:

√7 is irrational because 7 is not a perfect square, and its square root cannot be expressed as a fraction.

√100 is rational because 100 is a perfect square (10^2), and its square root is a whole number, 10.