Question

Simplify (√5+√2)power 2​

Answer 1

Question:-

➡ Simplify $\sf (\sqrt{5} + \sqrt{2})^{2}$

Answer:-

➡$\sf 7 +2\sqrt{10}$

Solution:-

⭐By using the following identities we will simplify the sum.

➡(a + b)² = a² + 2ab + b²

➡Now we will simplify,

➡$\sf (\sqrt{5}^{2}) + 2(\sqrt{5})(\sqrt{2}) + (\sqrt{2}^{2}) \\ =5 + 2 + 2\sqrt{10} \\ =7+2\sqrt{10}$

Hence, simplified.

Some identities:-

• a² - b² = (a-b) (a+b)
• (a+b)² = a² + 2ab + b²
• a² + b²= (a + b)² - 2ab
• (a + b + c)² = a² + b² +c² +2ab +2bc +2ac
• (a-b-c)² = a² + b² +c² - 2ab 2bc - 2ac
• (a + b)³ = a³ + 3a²b +3ab² +b³

✒Through this identities we can solve evry algebric expression.

Answer 2

Answer:

$7 + 2 \sqrt{10}$

Step-by-step explanation:

Using $\sf{(a+b)^2=a^2+b^2+2ab}$

${( \sqrt{5})}^{2} + {( \sqrt{2} )}^{2} + 2 \times \sqrt{5} \times \sqrt{2} \\ \\ 7 + 2 \sqrt{10}$

Hope it helps u

Have a great day ahead

Annyeong