Section 7.1 Radical Expressions Integrated Math Section 7.1 Radical Expressions

Square root- -finding a number, when squared, equals the number you are finding the square root of. 5 2 =5 Squaring and “square rooting” are opposite operations!

If a number is written in radical form, never precede the radical with ± . 36 = 6 − 36 =−6

Simplified radical expression- a radical expression with no perfect root factors in the radicand and no radicals in the denominator

Principal square root- the positive square root of a number

There are no square roots of a negative number! −# −# = +# +# +# = +# The only way to get a negative product is to multiply a negative number times a positive number (never squaring a number)

Cube root-finding a number, when cubed, equals the number you are finding the cube root of. 3 125 5 The cube root of 125 is 5 because 5×5×5=125

3 −8 =−2 3 1000 =10 You can take the cube root of a negative number. Recall −2 −2 −2 =−8 So… 3 −8 =−2 3 1000 =10

The 𝑛 𝑡ℎ root of a number (b) is a solution of the equation 𝑥 𝑛 =𝑏 5 1 =1 4 81 =3 5 −32 =−2

The index must always be a positive number.

When there is no index with a radical sign the number is an invisible 2 the radical means square root

When the radicand is zero, the answer will be zero regardless of the index

Simplifying the square root radical means there are no perfect squares under the radical sign 8 = 2∙2∙2 =2 2

Simplify #1 72 𝑥 3 𝑦 5 = 2×36× 𝑥 2 ×𝑥× 𝑦 4 ×𝑦 = 6𝑥 𝑦 2 2𝑥𝑦 #2 3 750 𝑥 10 𝑦 12 𝑧 4 = ?

Simplifying a fraction under the radical means there is no radical in the denominator. This can be done by #1 taking the root of the numerator and denominator #2 reducing the fraction #3 rationalizing the denominator

Fractions in the radicand #1 16 25 = ? #2 𝑥 7 𝑦 4 = ? #3 3 8 𝑦 6 = ? #4 14 5