roots

16

32

64

128

256

= 512

1024

121

144

169

196

225

256

289

= 324

= 361

= 400

625

8

= 27

125

216

343

512

729

1,000

To approximate the value of a root, find the squares that it lies between andesti␣mate.

To simplify any square root, rewrite the root as a product of its factors inside the radical and simplify any pairs that lie within.

To simplify complex square roots, the terms within the radical must be combined!

Complex square roots can often be simplified by factoring out terms in common to both terms within the radical.

– Terms that contain the same radical can be added or subtracted.

To multiply square roots, combine the terms under a single radical and multiply.

To divide square roots, break down the radicals, cancel out like terms, and simplify.

• Radicals cannot be left in the denominator of a fraction. •
• To rectify the situation, multiply the top and bottom of the fraction by the square root that appears inthe denominator.

Denominators that contain the sum or difference of a square root and another term cannot be simplified by the technique demonstrated above

• .• To simplify an expression such as7, it must be multiplied by the conjugate of its denominator. 5−3(1)
• Put another way, the conjugate of an expression is formed by changing its sign. T
• Mathematically, the difficulty of conjugating can be reduced by factoring the difference between perfect
• squares:

Recall that numbers with fractioned exponents can be expressed as roots. The denominator of the exponent determines the root of the base and the numerator determines what power to raise this root to.

There are two ways to take the square root of a decimal. What Squared Equals the Square Root?• In most instances, the easiest way to take the square root of decimal is to ask yourself “what times what would equal the square root?”