Question

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Answer 1

√5

Explanation:

Given:

`\displaystyle \large{5/ √(5)}`

Which can be rewritten as:

`\displaystyle \large{(5)/(√(5))}`

To find:

• Simplified form

To find simplified form of the expression, keep in mind that surds should not remain as denominators. Therefore, what we have to do is to multiply both numerator & denominator by the surd itself so the denominator will be cleared as rational number.

`\displaystyle \large{(5\cdot √(5))/(√(5)\cdot √(5))}`

We know that if same surds multiply each other, the surd will be canceled and remains only the insides. To express it in math, it can be as:

`\displaystyle \large{√(a)\cdot √(a) = \left(√(a)\right )^2 =a}`

Therefore:

`\displaystyle \large{(5√(5))/(5)}`

Cancel 5:

`\displaystyle \large{√(5)}`

Henceforth, the simplified expression is √5