Multiplication of Numbers with Square Roots

Q.

If x= 9+4√5 then find the value of √x-1/√x

Q.

If $a$ and $b$ are rational numbers.
$\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}$
find $a$ and $b$.

Q.

If a=, 2+, root3 then find the value of a-1/a

Q.

Rationalize the denominator of $\frac{4}{2+\surd 3+\surd 7}$

Q.

6-4√2/6+4√2. Rationalise

Q.

If $x=1-\sqrt{2}$ , find the value of $(x-\frac{1}{x}{)}^3$

Q.

Prove that 1/2+√3 + 2/√5-√3 + 1/2-√5=0

Q.

Rationalise :

Root 3 + root 2 by 5 + root 2

Q.

Simplify:-

⁴√12×⁷√6

Q.

Evaluate {√(5+2√6)} + {√(8-2√15)}

Q.

If $x=\sqrt{(p+q)}+\sqrt{(p-q)}÷\left[\sqrt{(p+q)}-\sqrt{(p-q)}\right]$ then find the value of $q{x}^2-2px+q$

Q.

The difference between the sides at right angles in a right angled triangle is 14 cm. The area of the triangle is 120sq.cm. find the perimeter.

Q. The value of \sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}} is

Q.

The number ${(1+\sqrt{3})}^2$ is a/an ____________.

1. natural number

2. rational number

3. irrational number

4. integer

Q.

√5+1/√5-1+√5-1/√5+1

Please solve with reason...

Q.

The measure of one side of a right triangle is 4.2m. If the difference of the lengths of hypotenuse and other is 14m, find the sides and area of the triangle.

Q.

Simplify 6/2√3-√6+√6/√3+√2-4√3/√6-√2

Q.

If √5+1/√5-1 y=√5-1/√5+1

find x2+y2

Q. Simplify:

(i) $({16}^{-1/5}{)}^{5/2}$

(ii) $\sqrt[5]{{\left(32\right)}^{-3}}$

(iii) $\sqrt[3]{(343{)}^{-2}}$

(iv) $(0.001{)}^{1/3}$

(v) $\frac{(25{)}^{3/2}\times (243{)}^{3/5}}{(16{)}^{5/4}\times (8{)}^{4/3}}$

(vi) ${\left(\frac{\sqrt{2}}{5}\right)}^8÷{\left(\frac{\sqrt{2}}{5}\right)}^{13}$

(vii) ${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^{-4}}\right)}^{7/2}\times {\left(\frac{5^{-2}\times 7^3}{5^3\times 7^{-5}}\right)}^{-5/2}$

Q.

If √[18-6√5] =√a-√b, then prove a + b= 18

Q.

Simplify√72-√800-√18

Q. find the value of a and b a+b√15=√5+√3/√5-√3

Q.

Find the value of $(\sqrt{2}+\sqrt{2})(\sqrt{2}-\sqrt{2})$.

1. 1

2. 2
3. 3
4. 0

Q. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find its shortest altitude.

Q.

Simplify the following (25)^3\2 × (243)^3\5 ÷ (16)^5\4 × (8)^4\3

Q.

³√3 or ⁴√4 which is greater?

Q.

Sir/ma'am

How will this equation be simplified. 4√3×4√3.

Q.

The perimeter of a right triangle is 24 cm. If it's hypotenuse is 10cm.Find its area

Q.

An unequal side of an isosceles triangle is 24 cm and its area is 60cm ² find the perimeter of isosceles triangle .

Q.

Simplify

12√18 - 6√20 - 3√50 + 8√45