why root7/16 equals to root 7/4
To solve the equation `(√7)/(16) = (√7)/(4)`, we can follow these steps:
Step 1: Simplify the denominators:
The denominator on the left side is 16, and on the right side is 4.
Step 2: Express both denominators as a common denominator:
We can express both 16 and 4 as their least common multiple (LCM), which is also 16.
Step 3: Multiply both the numerator and denominator of the left side by 1 (16/16) to achieve the common denominator:
`(√7)/(16) * (16/16) = (√7 * 16) / (16 * 16)`
Step 4: Simplify the expression on the left side:
`(√7 * 16) / (16 * 16) = (16√7) / 256`
Step 5: Simplify the expression:
By dividing both the numerator and denominator by their greatest common divisor (GCD), which is 16, we get:
`(16√7) / 256 = √7 / 16`
Therefore, `(√7)/(16) = (√7)/(4)` simplifies to `(√7)/(16) = (√7)/(4) = √7 / 16`
To understand why √7/16 is equal to √7/4, let's break down the math step by step.
First, let's simplify both fractions:
√7/16
To simplify the fraction on the right-hand side, we need to find a common factor between the numerator and the denominator. In this case, the number 4 is a common factor. When we divide both the numerator and the denominator by 4, we get:
(√7/4) * (1/4)
Now, let's simplify the fraction in the parentheses:
(√7/4) * (1/4)
To multiply fractions, we multiply the numerators and multiply the denominators:
(√7 * 1) / (4 * 4)
Simplifying both the numerator and the denominator, we get:
√7/16
Therefore, √7/16 is equal to √7/4.