Multiplying Radicals with Variables

Front

What is a radical?

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root.

Front

How do you simplify √(a^2)?

Back

√(a^2) = a, assuming a is non-negative.

Front

What is the product of two radicals?

Back

The product of two radicals can be simplified by multiplying the numbers inside the radicals: √a * √b = √(a*b).

Front

How do you multiply a radical by a variable?

Back

To multiply a radical by a variable, treat the variable as a coefficient: √a * b = b√a.

Front

What is the simplified form of √(xy)?

Back

√(xy) = √x * √y.

Front

How do you simplify √(a^2b)?

Back

√(a^2b) = a√b.

Front

What is the rule for multiplying radicals with coefficients?

Back

When multiplying radicals with coefficients, multiply the coefficients and then the radicals: a√b * c√d = (a*c)√(b*d).

Front

What is the simplified form of √(x^4)?

Back

√(x^4) = x^2.

Front

How do you simplify √(64x^9)?

Back

√(64x^9) = 8x^4√x.

Front

What is the result of 6√2 ⋅ 5√14?

Back

6√2 ⋅ 5√14 = 30√(2*14) = 30√28 = 60√7.