Simplify the expression: (5 + 7)( 2 + 5) - Vidyadip

Question

Simplify the expression: (5 + $\sqrt{7}$)( 2 + $\sqrt{5}$)

✓

Answer

It is given that,
(5 + $\sqrt{7}$)(2 + $\sqrt{5}$) [opening both the brackets using distributive property]
= (5 $\times$ 2)+(5 $\times$ $\sqrt{5}$) +( $\sqrt{7}$ $\times$ 2)+( $\sqrt{7}$ $\times$ $\sqrt{5}$)
= 10 + 5$\sqrt{5}$ + 2$\sqrt{7}$ + $\sqrt{7 \times 5}$

= 10 + 5$\sqrt{5}$ + 2$\sqrt{7}$ + $\sqrt{35}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Number systems→Number systems — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

A cylinder of radius $12\ cm$ contains water to a depth of $20\ cm$. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by $6.75\ cm$. Find the radius of the ball. $\Big(\text{Use }\pi=\frac{22}{7}\Big).$

If the volume of a right circular cone of height 9 cm is 48$\pi {~cm}^3$, find the diameter of its base.

Simplify $\Bigg[\Big\{(256)^{-\frac{1}{2}}\Big\}^{-\frac{1}{4}}\Bigg]^2.$

Write four solutions of the equation: $\pi x + y = 9$

There are $50$ students in a class, of which $40$ are boys. The average weight of the class is $44\ kg$ and that of the girls is $40\ kg.$ Find the average weight of the boys.

The surface areas of two spheres are in the $1 : 4$. Find the ratio of their volumes.

Assuming that $x, y, z$ are positive real numbers, simplify the following: $\Big(\text{x}^{-\frac{2}{3}}\text{y}^{-\frac{1}{2}}\Big)^2$

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute-angled.

Write $(3 a+4 b)^3$ in the expanded form.

Simplify: $\Big(\frac{32}{243}\Big)^{-\frac{4}{5}}$