Question

Write √50 in the form k√/2, where k is an integer.

Answer 1

You start off by simplifying root 50, as it is not a surd.

Look for a square number that fits into 50
- (root 25) and (root 2)

Find the square root of 25
= 5

So therefore the answer is 5 root 2.

Answer 2

`5√(2)`

k = 5

Explanation:

Given:

`√(50)`

Rewrite 50 as 25 · 2:

`\implies √(25 \cdot 2)`

`\textsf{Apply the radical rule} \quad √(ab)=√(a)√(b):`

`\implies √(25)√(2)`

Rewrite 25 as 5²:

`\implies √(5^2)√(2)`

`\textsf{Apply the radical rule} \quad √(a^2)=a, \quad a \geq 0:`

`\implies 5√(2)`

Therefore, k = 5.