Question

Simplify 4+√6/4-√6. +. 4-√6/4+√6

Answer 1

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Answer 2

Answer: On simplifying    $\frac{4+\sqrt{6} }{4-\sqrt{6} }+\frac{4-\sqrt{6} }{4+\sqrt{6} }$ we get 3.2

Step-by-step explanation:

Given:We have given    $\frac{4+\sqrt{6} }{4-\sqrt{6} }+\frac{4-\sqrt{6} }{4+\sqrt{6} }$

To find:We have to simplify the expression.

Explanation:

Step 1:As we have given, $\frac{4+\sqrt{6} }{4-\sqrt{6} }+\frac{4-\sqrt{6} }{4+\sqrt{6} }$

Step 2:Taking LCM of denominators we get,

⇒    $\frac{(4+\sqrt{6})^{2}+(4-\sqrt{6})^{2} }{(4-\sqrt{6)(4+\sqrt{6)} } }$

⇒   $\frac{4^{2}+2(4)(\sqrt{6})+(\sqrt{6})^{2}+4^{2}-2(4)(\sqrt{6})+(\sqrt{6})^{2} }{(4)^{2}-(\sqrt{6})^{2} }$

⇒    $\frac{16+8\sqrt{6}+6+16-8\sqrt{6}+6 }{16-6}$

⇒    $\frac{16+6+16-6}{10}$

⇒     $\frac{16+16}{10}$

⇒      $\frac{32}{10}$

⇒      $3.2$

∴ On simplifying    $\frac{4+\sqrt{6} }{4-\sqrt{6} }+\frac{4-\sqrt{6} }{4+\sqrt{6} }$ we get 3.2

The principal square root of  a  is the non negative number that, when multiplied by itself, equals  a . It is written as a radical expression  $\sqrt{a}$ , with the symbol called a radical, over the term  a , called the radicand.  

.  When the square root of a number is squared, the result is the original number. Since  $4^{2}$=16 , the square root of  16  is  4 .The square root function is the inverse of the squaring function just as subtraction is the inverse of addition. To undo squaring, we take the square root.

In general terms, if  a  is a positive real number, then the square root of  a  is a number that, when multiplied by itself, gives  a . The square root could be positive or negative because multiplying two negative numbers gives a positive number. However, the √ symbol denotes just the non-negative result, or so-called principal square root. The square root obtained using a calculator is the principal square root.

The principal square root is the non negative number that when multiplied by itself equals  a . The principal square root of  a  is written as  $\sqrt{a}$ . The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression.

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