Question

4 root 2 minus 2 root 8 +3/root2

Answer 1

hope this will help you

Answer 2

Complete Question:

$4\sqrt{2} -2\sqrt{8} +\frac{3}{\sqrt{2} }$

Answer:

The simplification of the equation is $\frac{3\sqrt{2} }{2}$

Explanation:

Given:

$4\sqrt{2} -2\sqrt{8} +\frac{3}{\sqrt{2} }$

To Find:

Simplify the equation

Solution:

$4\sqrt{2} -2\sqrt{8} +\frac{3}{\sqrt{2} }$

Taking $\sqrt{2}$ common as LCM

This makes,

$4\sqrt{2} * \sqrt{2} = 8$

$2\sqrt{8} * \sqrt{2} = 2\sqrt{16}$

Thus, the fraction now becomes,

$=\frac{8-2\sqrt{16} +3}{\sqrt{2}}$

$=\frac{8-2*4 +3}{\sqrt{2}}$

$=\frac{8-8 +3}{\sqrt{2}}$

$=\frac{3}{\sqrt{2}}$

Rationalizing the denominator of the equation,

$=\frac{3}{\sqrt{2}} *\frac{\sqrt{2} }{\sqrt{2} }$

$= \frac{3\sqrt{2} }{2}$

Rationalizationation:

• In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator.
• To rationalize the denominator, a variety of strategies are available.
• Making something more effective is the exact meaning of the term rationalize.
• Its use in mathematics entails simplifying and reducing the equation to its more useful form.
• A radical or imaginary number can be removed from the denominator of an algebraic fraction by a procedure known as rationalization.
• Specifically, eliminate the radicals from the fraction's denominator, leaving only the rational integer.

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