Add and subtract radicals

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you add radicals with the same index?

Back

You can add radicals with the same index by combining their coefficients. For example, 2√5 + 4√5 = (2 + 4)√5 = 6√5.

Front

What is the first step in subtracting radicals?

Back

The first step is to simplify the radicals if possible, then subtract the coefficients of like radicals.

Front

Simplify: √18 - √8

Back

√18 - √8 = √(9*2) - √(4*2) = 3√2 - 2√2 = (3 - 2)√2 = √2.

Front

What is the result of (5√3) + (6√3)?

Back

(5√3) + (6√3) = (5 + 6)√3 = 11√3.

Front

How do you simplify √300 + √75?

Back

√300 + √75 = √(100*3) + √(25*3) = 10√3 + 5√3 = (10 + 5)√3 = 15√3.

Front

What is the result of adding and subtracting the following: 4√7 - 10√7 + 7√7?

Back

4√7 - 10√7 + 7√7 = (4 - 10 + 7)√7 = 1√7 = √7.

Front

What is the index of a radical?

Back

The index of a radical indicates the degree of the root. For example, in √x, the index is 2 (square root), and in ∛x, the index is 3 (cube root).

Front

Can you add radicals with different radicands?

Back

No, you cannot add radicals with different radicands unless they can be simplified to have the same radicand.

Front

What is the simplified form of √50?

Back

√50 = √(25*2) = 5√2.