Question

Please tell the answer

Answer 1

Answer:

√5²+2² square and root are cancelled so 5+2 is left =7

Answer 2

Answer:

1. 7 + 2√10

2. rational

3. $\frac{8}{27}$

4. -6

5. 998000

6. x = -$\frac{5}{2\\}$

7. x = 110

Step-by-step explanation:

1) (√5 + √2)² =

expand using (a+b)² = a²+2ab+b² where a = √5 and b = √2

5 + 2√10 + 2 = 7 + 2√10

2. (3 + √23) - √23 =

by associative property of addition, regrouping does not change the answer so...

3 + (√23 - √23) ... √23 - √23 cancels out leaving just 3

3 is rational therefore the answer is rational

3. $(\frac{81}{16})^{-\frac{3}{4} }$

negative exponent means you take the reciprocal of the base

$(\frac{16}{81})^{\frac{3}{4} }$

When you have something to the $\frac{a}{b}$ power, b is the index of a square root and a is the power of the entire thing (for example $a^{\frac{m}{n} }$ = $(\sqrt[n]{a})^{m}$

So we will have $(\sqrt[4]{\frac{16}{81}})^{3}$

The fourth root of 16 is 2 and the fourth root of 81 is 3

So $(\frac{2}{3} )^{3}$ = $\frac{8}{27}$

4. 5x - 4x²+3 at x = -1

5(-1) - 4(-1)² + 3 =

-5 - 4(1) + 3 =

-5 - 4 + 3 = -6

5. (999)² - (1)²

Use a²-b² = (a+b)(a-b) where a is 999 and b is 1

(999+1)(999-1) = 1000(998) = 998000

6. p(x) = 2x + 5

To find the zeroes, solve for x when p(x) = 0

0 = 2x + 5

-2x = 5

x = -$\frac{5}{2\\}$

7. Value of ∠PSR is 56° since ∠QPS and ∠PSR are alternate side interior angles, they are congruent

Sum of angles in a triangle is 180° so m∠x + m∠PSR + m∠R = 180°

m∠x + 56° + 14° = 180

m∠x = 110°