Answer :
To simplify \(\sqrt{8}\), we can follow these steps:
1. Prime Factorization:
Begin by expressing 8 as a product of its prime factors.
[tex]\[ 8 = 2 \times 4 = 2 \times 2 \times 2 \][/tex]
2. Rewrite Under the Root:
Rewrite the square root of 8 using these prime factors.
[tex]\[ \sqrt{8} = \sqrt{2 \times 2 \times 2} \][/tex]
3. Group Factors into Pairs:
Notice that within the square root, there is a pair of 2s (since \(2 \times 2 = 4\)).
[tex]\[ \sqrt{8} = \sqrt{(2 \times 2) \times 2} = \sqrt{4 \times 2} \][/tex]
4. Simplify the Square Root of a Perfect Square:
Simplify \(\sqrt{4 \times 2}\). Since the square root of 4 is 2, we can separate it out of the square root.
[tex]\[ \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2} \][/tex]
Therefore, the simplified form of \(\sqrt{8}\) is:
[tex]\[ \sqrt{8} = 2\sqrt{2} \][/tex]
1. Prime Factorization:
Begin by expressing 8 as a product of its prime factors.
[tex]\[ 8 = 2 \times 4 = 2 \times 2 \times 2 \][/tex]
2. Rewrite Under the Root:
Rewrite the square root of 8 using these prime factors.
[tex]\[ \sqrt{8} = \sqrt{2 \times 2 \times 2} \][/tex]
3. Group Factors into Pairs:
Notice that within the square root, there is a pair of 2s (since \(2 \times 2 = 4\)).
[tex]\[ \sqrt{8} = \sqrt{(2 \times 2) \times 2} = \sqrt{4 \times 2} \][/tex]
4. Simplify the Square Root of a Perfect Square:
Simplify \(\sqrt{4 \times 2}\). Since the square root of 4 is 2, we can separate it out of the square root.
[tex]\[ \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2} \][/tex]
Therefore, the simplified form of \(\sqrt{8}\) is:
[tex]\[ \sqrt{8} = 2\sqrt{2} \][/tex]
