Question

1 + root 2 / 3 - 2 root 2 rationalise ​

Answer 1

Answer:

 7 +5$\sqrt{2}$ is the required value.

Step-by-step explanation:

Explanation:

Given, $\frac{1+\sqrt{2} }{3 - 2\sqrt{2} }$

According to the question we need to rationalize the denominator.

• Rationalization- An irrational number is rationalized, or changed into a number that can be stated as the ratio of two integers, through the process of rationalization.

• When you rationalize an equation, we remove any surpluses from the fractions' bottom. Typically, when we are requested to rationalize or simplify an expression, it also suggests that we should do so.

Step 1:

We have , $\frac{1+\sqrt{2} }{3 - 2\sqrt{2} }$

Now, we multiplying  both numerator and denominator by $3 + 2\sqrt{2}$

⇒$\frac{1 + \sqrt{2} }{3 - 2\sqrt{2} }$ × $\frac{3 + 2\sqrt{2} }{3 +2\sqrt{2} }$ =$\frac{(1 +\sqrt{2} )(3 + 2\sqrt{2} )}{(3^2 - (2\sqrt{2} )^2)}$

⇒$\frac{(1 +\sqrt{2} )(3 + 2\sqrt{2} )}{(3^2 - (2\sqrt{2} )^2)}$ = $\frac{(1 +\sqrt{2} )(3 + 2\sqrt{2} )}{(9 - 8)}$ = $(1 +\sqrt{2} )(3 + 2\sqrt{2} )$

⇒$(1 +\sqrt{2} )(3 + 2\sqrt{2} )$ = 3 + $2\sqrt{2}$ + 3$\sqrt{2}$ + 2 × 2  = 7 +5$\sqrt{2}$

Final answer:

Hence,  7 +5$\sqrt{2}$ is the required value for the given question.

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Answer 2

Correct Question:

Rationalize the number: $\frac{1+\sqrt2}{3-2\sqrt2}$

Answer:

The rationalized result of the number is found to be: $7+5\sqrt2$

Step-by-step explanation:

Rationalization:

We apply rationalization techniques to radical expressions. Suppose you can "rationalize" the denominator and convert it to  a rational number. This requires an identity from the  square root.

If the denominator of an expression contains a term that has a square root (or a number under the root symbol), the process of converting it to an equivalent expression whose denominator is a rational number is called denominator rationalization.

Rationalizing the given number:

The given number to us is: $\frac{1+\sqrt2}{3-2\sqrt2}$

In order to rationalize the number, we will find the conjugate of denominator, found to be: $3+2\sqrt2$

Multiplying and dividing by $3+2\sqrt2$, we get:

$\frac{1+\sqrt2}{3-2\sqrt2}\times\frac{3+2\sqrt2}{3+2\sqrt2}$

or we can say:

$\frac{(1+\sqrt2)(3+2\sqrt2)}{9-4(2)}=\frac{3+2\sqrt2+4+3\sqrt2}{9-8}$

Simplifying this, we get:

$=\frac{7+5\sqrt2}{1}$

Thus, the rationalized result of the given number is found to be: $7+5\sqrt2$.

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