Similar or like Surds

Q. Question 18
The product $\sqrt[3]{32}.\sqrt[4]{42}.\sqrt[12]{1232}$ equals to
Thinking process
Take the LCM of indices of three irrational numbers. Then, convert all individually in the from whose index will be equal to LCM.

A) $\sqrt{2}$
B) $2$
C) $\sqrt[12]{122}$
D) $\sqrt[12]{1232}$

Q.

Which of the following is NOT a pair of like surds

1. $(3\times \sqrt[2]{280})$, $(4\times \sqrt[2]{2245})$

2. $(2\times \sqrt[2]{263})$, $(3\times \sqrt[2]{212})$

3. $(7\times \sqrt[2]{2128})$, $(4\times \sqrt[2]{2242})$

4. $(5\times \sqrt[2]{2108})$, $(6\times \sqrt[2]{2192})$

Q.

Find $(5+\sqrt{7})(2+\sqrt{5})$ .Is it rational? [4 MARKS]

Q.

Find the value of ${(\sqrt{3}+\sqrt{7})}^2$. Is it rational? [4 MARKS]

Q. (√6)²ⁿ+⁴ =216
I hv solved this sum like this -

• (6²)²ⁿ+⁴ = 6³
• 6⁴ⁿ+8= 6³
• As bases are same ; powers will also be same .
• 4n+8 = 3
• 4n= -5

Therefore , n= -5/4
Can you please guide me where I have went wrong and why??

Q.

If 'a' and 'b' are rational numbers, then find the values of 'a' and 'b' given that $\frac{2+5\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3}$

1. a = 19 , b = 12

2. a = 12 , b = 19

3. a = 20 , b = 13

4. a = 9 , b = 2