simplify-11√112
To simplify −11√112, we want to break down the square root of 112 into its prime factors and then simplify by taking out any square numbers:
112 = 2 × 56
= 2 × 2 × 28
= 2 × 2 × 2 × 14
= 2 × 2 × 2 × 2 × 7
= 2^4 × 7
We have a perfect square, 2^4, which is 16. We can take the square root of this perfect square:
√112 = √(2^4 × 7)
= √(16 × 7)
= √16 × √7
= 4√7
Now we can replace √112 with 4√7 in the original expression:
−11√112 = −11 × 4√7
= −44√7
The simplified version of −11√112 is −44√7.