1.5 Simplify Square Roots and Solve.notebook
Warm Up
Solve by factoring.
2
1. 4x = 24x
2
2. 16x - 361 = 0
2
3. 20x = 25x + 4
2
4. 2x + 7x - 15 = 0
Warm Up
page 22
42. A rectangular picnic site measures 24 feet by
10 feet. You want to double the site's area by
adding the same distance x to the length and
the width. By what distance x should the length
and width be increased?
September 27, 2016
1.5 Simplify Square Roots and Solve.notebook
September 27, 2016
1.5 Solve Quadratics by Square Roots
I. Square Root of Positive Number
2
A number r is a square root of s if r = s
2
iff r = s
radical sign
radicand (number under the radical sign)
A positive number has TWO square roots:
and
2
= 10, since 10 = 100
2
= -10, since (-10) = 100
1.5 Simplify Square Roots and Solve.notebook
September 27, 2016
To simplify a radical (if you do not know the
root/answer), factor the radicand using prime factors
prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.
examples: √196
√ 80
TRY!
√450
√72
page 32
A square root is simplified when:
1) the radicand has NO perfect square factors
other than 1,
2) the radicand is NOT a fraction, and
3) NO radical is in the denominator.