Sure, let's simplify [tex]\( \sqrt{98} \)[/tex] step-by-step.
1. Factorize 98: First, we need to express 98 in terms of its prime factors.
[tex]\( 98 = 2 \times 49 \)[/tex]
2. Rewrite the square root: Using the property of square roots that [tex]\( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \)[/tex], we can rewrite [tex]\(\sqrt{98}\)[/tex] as:
[tex]\( \sqrt{98} = \sqrt{2 \times 49} \)[/tex]
3. Simplify the expression: Notice that 49 is a perfect square (since [tex]\( 49 = 7^2 \)[/tex]). We can further break down the expression:
[tex]\( \sqrt{2 \times 49} = \sqrt{2} \times \sqrt{49} \)[/tex]
4. Calculate the square root of 49: Since [tex]\(\sqrt{49} = 7\)[/tex], substitute this value back into the expression:
[tex]\( \sqrt{2} \times \sqrt{49} = \sqrt{2} \times 7 \)[/tex]
5. Combine the factors: This simplifies to:
[tex]\( 7 \sqrt{2} \)[/tex]
Therefore, the simplified form of [tex]\( \sqrt{98} \)[/tex] is [tex]\( 7 \sqrt{2} \)[/tex].
So, the correct answer is:
B. [tex]\( 7 \sqrt{2} \)[/tex]
