Transcript Simplifying Radicals

Simplifying Radicals
SPI 3102.2.1
Operate (add, subtract, multiply, divide, simplify, powers) with radicals and
radical expressions including radicands involving rational numbers and algebraic expressions.
Simplifying Radicals
• Until now, all of the square roots we have encountered
have been perfect squares.
• Other than perfect squares, the result of taking the
square root of a number results in a decimal answer.
• Unless otherwise specified, all answers from this point
on, will be written in simplest radical form. Decimal
answers will not be acceptable.
• We will also be simplifying cube roots, fourth roots,
etc. (nth roots).
Simplifying Radicals
Before we begin, there is some basic terminology you
will need to know.
radical
sign
index
n
x
radicand
If there is not an index written on the radical, the index
is understood to be 2, which means it is a square root.
Simplify.
50
25  2
5 2
Write 50 as the product of 2 numbers,
one of which is a perfect square.
Take the square root of the number that is a
perfect square; write that number in front of the
square root sign.
The number that is not a perfect square stays
under the radical sign.
Simplify.
Simplify.
98
99
49  2
9 11
7 2
3 11
Simplify.
700
Simplify.
98
100  7
49  2
10 7
7 2
What if the index is
larger than 2?
Simplify.
3
3
32
8 4
23 4
Write 50 as the product of 2 numbers,
one of which is a perfect CUBE.
Take the cube root of the number that is a
perfect cube; write that number in front of the
square root sign.
The number that is not a perfect cube stays
under the radical sign.
Simplify.
3
3
54
27  2
33 2
Simplify.
3
3
686
343  2
73 2
Simplify.
4
4
48
16  3
4
2 3
Simplify.
5
5
972
243  4
35 4