How to simplify. Steps Please.
-11sqrt112
To simplify the expression -11√112, we can follow these steps:
Step 1: Rewrite 112 as a product of its prime factors.
112 = 2 × 2 × 2 × 2 × 7
Step 2: Simplify the square root by taking out perfect square factors.
√(2 × 2 × 2 × 2 × 7) = √(2 × 2 × 2 × 2) × √7
Step 3: Simplify the perfect square factor.
√(2 × 2 × 2 × 2) = √(2² × 2²) = 2 × 2 = 4
Step 4: Rewrite the simplified square root and multiplying it by -11.
-11√(2 × 2 × 2 × 2) × √7 = -11 × 4 × √7
Step 5: Perform the multiplication.
-11 × 4 × √7 = -44√7
Therefore, the simplified form of -11√112 is -44√7.
To simplify the expression -11√112, follow these steps:
Step 1: Identify any perfect square factors in the radicand (the number under the square root):
In this case, 112 can be written as a product of its prime factors: 112 = 2 x 2 x 2 x 2 x 7 = 2^4 x 7.
Step 2: Group the perfect squares together:
In the prime factorization of 112, the perfect square is 2^4, since 2 x 2 x 2 x 2 = 16. Therefore, rewrite 112 as 16 x 7 under the square root sign.
Step 3: Simplify the expression:
-11√(16 x 7) = -11√16 x √7
The square root of 16 is 4, so this can be further simplified as:
-11 x 4√7 = -44√7
Therefore, -11√112 simplifies to -44√7.
-11√112
= -11√(16*7)
= -11√16√7
= -11*4√7
= -44√7