Multiplying Radicals with Variables

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

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

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

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

√(xy) = √x * √y.

√(a^2b) = a√b.

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

√(x^4) = x^2.

√(64x^9) = 8x^4√x.

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