Simplify the expression:
1/2*(square root of 112)
Ex: 90^1/2= 10^1/2 * 9^1/2
Answer: 3(10^1/2)
Simply the following surds
Factors of 112 is
2×2×2×2×7
So the answer is 4√7
By read 4 root 7
112=
2*56
2*2*28
2*2*2*14
2*2*2*2*7
sqrt 112= sqrt(16*7)=4*sqrt7
112 = 4 x 28
sqrt 112 = 2 sqrt 28
If sqrt112 is a multiplier of 1/2, the answer would be sqrt28.
Parentheses would have helped clarify where the sqrt112 goes.
Duh. I forgot to take another factor of 4 out.
sqrt 28 = 2 sqrt 7 etc
To simplify the expression 1/2 * √112, we can start by simplifying the square root of 112.
Step 1: Find the prime factorization of 112:
To determine the prime factorization, we divide 112 by the smallest prime numbers repeatedly until we can't divide anymore:
112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
The prime factorization of 112 is 2^4 * 7.
Step 2: Simplify the square root of 112:
Since the square root of a product is equal to the product of the square roots, we can break down the square root of 112 as follows:
√112 = √(2^4 * 7)
Using the property of square roots, we can separate the square root of 112 into the multiplication of separate square roots:
√112 = √(2^4) * √7
Step 3: Evaluate each square root:
The square root of 2^4 can be simplified to 2^(4/2) which equals 2^2. And the square root of 7 cannot be simplified further. Therefore:
√112 = 2^2 * √7
Step 4: Simplify the expression:
Now, let's simplify the expression 1/2 * (2^2 * √7):
1/2 * (2^2 * √7) = 1/2 * 2^2 * √7
= 1 * √7
= √7
Therefore, the simplified expression is √7.