Question

If root 3 = 1.732 and root 2 =1.414 then find the value of 1/ root 3- root 2

Answer 1

Concept:

Mathematics has 4 basic operations namely edition subtraction multiplication and division. Simplifying and expression means solving the expression to reduce it into its lowest form. Expanding and expression means to apply all the operations of mathematics and make a simple expression.

Given:

We are given that:

√ 3 = 1.732 and √2 =1.414

Find:

We need to find the value of:

1 / ( √3- √2 ).

Solution:

We will substitute the values of √2 and √3 in the expression:

1 / ( 1.732 - 1.414 )

Now we will solve it to get he value:

1 / ( 0.318 )

= 3.145.

Therefore, we get the value of 1 / ( √3- √2 ) as 3.145.

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Answer 2

Question: If $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$ then find the value of $\frac{1}{\sqrt{3}-\sqrt{2} }$.

Answer:

The value of $\frac{1}{\sqrt{3}-\sqrt{2} }$ is 3.146.

Step-by-step explanation:

Step 1 of 2

It is given that,

$\sqrt{3}=1.732$ and $\sqrt{2}=1.414$

Consider the given expression as follows:

$\frac{1}{\sqrt{3}-\sqrt{2} }$

Rationalize the expression as follows:

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

$\frac{\sqrt{3} +\sqrt{2} }{(\sqrt{3}-\sqrt{2} )(\sqrt{3}+\sqrt{2} )}$

Using the identity, $(a+b)(a-b)=a^2-b^2$, we get

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

Since $(\sqrt{3} )^2=3$ and $(\sqrt{2} )^2=2$.

⇒ $\frac{\sqrt{3} +\sqrt{2} }{3-2}$

On simplifying, we have

⇒ $\frac{\sqrt{3} +\sqrt{2} }{1}$

⇒ $\sqrt{3} +\sqrt{2}$

Step 2 of 2

Find the value of $\frac{1}{\sqrt{3}-\sqrt{2} }$.

From step 1, we have

$\frac{1}{\sqrt{3}-\sqrt{2} }=\sqrt{3}+\sqrt{2}$ . . . . . (i)

Substitute the values 1.732 for $\sqrt{3}$ and 1.414 for $\sqrt{2}$ on the right-hand side of the expression (i) as follows:

⇒ $\frac{1}{\sqrt{3}-\sqrt{2} }=1.732+1.414$

⇒ $\frac{1}{\sqrt{3}-\sqrt{2} }=3.146$

Final answer: The value of $\frac{1}{\sqrt{3}-\sqrt{2} }$ is 3.146.

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