How do you simplify radicals
√162
look for factors so that at least one of the factors is a perfect square.
e.g.
162 = 9 * 18
= 9 * 9 * 2
so √162 = √9 * √9 * √2
= 3*3*√2
= 9√2
You can always check your answer using a calculator.
Ok for √726
726/2 = 363
Then what
Is answer 11√6
726 = 2*363 ok but
2*363 = 2 * 3 * 121
BUT
121 = 11*11 :)
so we have
1*3*11*11
=11^2 * 6
so sqrt(11^2 * 6) = 11 sqrt 6
To simplify radicals, you need to find the largest perfect square that is a factor of the number inside the radical.
To simplify √162, you need to find the largest perfect square that can be divided evenly into 162.
Start by finding the prime factorization of 162.
162 = 2 * 81
81 is a perfect square because it is 9 * 9.
Now rewrite the expression as √(2 * 81).
Since √(81) = 9, you can simplify further to become 9√2.
So, √162 can be simplified to 9√2.