Question

simplify the following expressions(√3+√7)² ​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

(10+2√21)

Step-by-step explanation:

To simplify

• ${( \sqrt{3} + \sqrt{7} )}^{2}$

Clearly, it's in the form of,

• ${(x + y)}^{2}$

Where,

• x = √3
• y = √7

But, we know that,

• ${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

Therefore, we will get,

$= {( \sqrt{3} )}^{2} + 2( \sqrt{3} )( \sqrt{7} ) + {( \sqrt{7} )}^{2} \\ \\ = 3 + 2 \sqrt{3 \times 7} + 7 \\ \\ = 10 + 2 \sqrt{21}$

Hence, the required answer is (10+2√21).

Some more identities:-

• ${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$
• ${(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx$
• ${(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$
• ${(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$