Question

WILL FAN AND MEDAL!!

In complete sentences, explain why and how to simplify the following radicals:

1) √63

2) √96

3) √x^23

4) √40x^5y

Answer 1

heard of `prime factorization` before ?

Answer 2

\(\large \sqrt{63} = \sqrt{9 \times 7} = \sqrt{3^2\times 7} = 3\sqrt{7}\)

Answer 3

Step1 :
The goal here is to find the prime factors of 63. Since 63 is not prime, find two numbers that multiply to 63. How about 9 and 7? Since 7 is prime, it doesn’t need to be factored anymore. However, 9 may be written as 3 times 3. Three is also a prime number. Therefore, the prime factors of 63 are 7, 3, and 3.

Answer 4

Step2 :
Next you need to look for pairs of factors. For 63, there is only one pair of factors inside the radical: 3 times 3. Since the square root of 3 times 3 is the same as 3, a pair of factors inside the radical becomes a single factor outside the radical. Any remaining factors stay inside the radical. The square root of 63 simplifies to 3 times the square root of 7.

Answer 5

See if you can work the remaining problems :)