Question

question
go step by step to reduce the radical.
\sqrt{48}
\sqrt{\square} \sqrt{\square}

Explanation:

Step1: Factor 48 into perfect square and other

We know that \( 48 = 16\times3 \), where 16 is a perfect square. So we can rewrite \( \sqrt{48} \) as \( \sqrt{16\times3} \).

Step2: Use property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0,b\geq0 \)), we get \( \sqrt{16\times3}=\sqrt{16}\times\sqrt{3} \).

Step3: Simplify \( \sqrt{16} \)

Since \( 4^2 = 16 \), \( \sqrt{16}=4 \). So the simplified form is \( 4\sqrt{3} \). But for the given blanks, we need to fill the factors. So the first blank is 16 and the second blank is 3.

Answer:

The first blank is 16 and the second blank is 3, so \( \sqrt{48}=\sqrt{16}\sqrt{3} \)