Simplify [tex]\(\sqrt{50} - \sqrt{98} + \sqrt{162}\)[/tex].

A. [tex]\(\sqrt{114}\)[/tex]
B. [tex]\(\sqrt{14}\)[/tex]
C. [tex]\(2 \sqrt{}\)[/tex]



Answer :

To simplify the expression [tex]\(\sqrt{50} - \sqrt{98} + \sqrt{162}\)[/tex], we can express each term in its simplified form:

1. Simplify [tex]\(\sqrt{50}\)[/tex]:
[tex]\[ \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \][/tex]

2. Simplify [tex]\(\sqrt{98}\)[/tex]:
[tex]\[ \sqrt{98} = \sqrt{49 \cdot 2} = \sqrt{49} \cdot \sqrt{2} = 7\sqrt{2} \][/tex]

3. Simplify [tex]\(\sqrt{162}\)[/tex]:
[tex]\[ \sqrt{162} = \sqrt{81 \cdot 2} = \sqrt{81} \cdot \sqrt{2} = 9\sqrt{2} \][/tex]

Now, combining these simplified terms:
[tex]\[ \sqrt{50} - \sqrt{98} + \sqrt{162} = 5\sqrt{2} - 7\sqrt{2} + 9\sqrt{2} \][/tex]

Next, combine the terms involving [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ (5 - 7 + 9)\sqrt{2} = 7\sqrt{2} \][/tex]

Hence, the simplified form of the given expression is:
[tex]\[ \sqrt{50} - \sqrt{98} + \sqrt{162} = 7\sqrt{2} \][/tex]

We can also confirm this numerically:

- Approximate value of [tex]\(5\sqrt{2} \approx 7.071\)[/tex]
- Approximate value of [tex]\(7\sqrt{2} \approx 9.899\)[/tex]
- Approximate value of [tex]\(9\sqrt{2} \approx 12.728\)[/tex]

Combining them:
[tex]\[ 7.071 - 9.899 + 12.728 \approx 9.899 \][/tex]

The simplest answer among the options is:
[tex]\[ 7\sqrt{2} \approx 9.899 \][/tex]

Thus, the correct simplified form is:
[tex]\[ \boxed{7\sqrt{2}} \][/tex]