Find sum of the following surds- x-x- y-y- 3-x3- 4-y3

The sum of the given surds can be determined as follows: x√( x ) +y√( y ) +3√( x^ 3 ) +4√( y^ 3 ) =x√( x ) +y√( y ) +3√( x^ 2 × x ) +4√( y^ 2 × y ) =x√( x ) ...

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Byju's Answer

Standard IX

Mathematics

Addition and Subtraction of Surds

Find sum of t...

Question

Find sum of the following surds:
$x \sqrt{x}, y \sqrt{y}, 3 \sqrt{x^{3}}, 4 \sqrt{y^{3}}$

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Solution

The sum of the given surds can be determined as follows:
$x \sqrt{x} + y \sqrt{y} + 3 \sqrt{x^{3}} + 4 \sqrt{y^{3}} = x \sqrt{x} + y \sqrt{y} + 3 \sqrt{x^{2} \times x} + 4 \sqrt{y^{2} \times y} = x \sqrt{x} + y \sqrt{y} + 3 x \sqrt{x} + 4 y \sqrt{y}$
$= \sqrt{x} (x + 3 x) + \sqrt{y} (y + 4 y) = 4 x \sqrt{x} + 5 y \sqrt{y}$

Hence, $x \sqrt{x} + y \sqrt{y} + 3 \sqrt{x^{3}} + 4 \sqrt{y^{3}} = 4 x \sqrt{x} + 5 y \sqrt{y}$ .

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Find sum of the following surds:x√x,y√y,3√x3,4√y3

The sum of the given surds can be determined as follows:x√x+y√y+3√x3+4√y3=x√x+y√y+3√x2×x+4√y2×y=x√x+y√y+3x√x+4y√y=√x(x+3x)+√y(y+4y)=4x√x+5y√y Hence, x√x+y√y+3√x3+4√y3=4x√x+5y√y.

Find sum of the following surds:
$x \sqrt{x}, y \sqrt{y}, 3 \sqrt{x^{3}}, 4 \sqrt{y^{3}}$