Question

every positive number has a square root. in fact, it has two square roots — one positive and one negative. 3 and -3 are both square roots of 9 because 3² = 9 and (-3)² = 9. how will we know which number is meant by √9? to avoid confusion we use the symbol -√ for the negative square root and save √ for the positive square root. √a means \the positive square root of a.\ -√a means \the negative square root of a.\ find each square root. -√64 = -8 -√10,000 = -√(1/9) = √121 = √4,900 = -√(121/49) = -√25 = √.0036 = -√(4/81) = √1 = -√400 = √(9/2500) = -√441 = -√1600 = √(16/900) = -√.09 = √.25 =

Explanation:

Step1: Recall square - root definition

If $x^{2}=a$, then $x = \pm\sqrt{a}$, where $\sqrt{a}$ is the positive square - root and $-\sqrt{a}$ is the negative square - root.

Step2: Calculate $-\sqrt{10000}$

Since $100^{2}=10000$, then $-\sqrt{10000}=-100$.

Step3: Calculate $-\sqrt{\frac{1}{9}}$

Since $(\frac{1}{3})^{2}=\frac{1}{9}$, then $-\sqrt{\frac{1}{9}}=-\frac{1}{3}$.

Step4: Calculate $\sqrt{121}$

Since $11^{2}=121$, then $\sqrt{121}=11$.

Step5: Calculate $\sqrt{4900}$

Since $70^{2}=4900$, then $\sqrt{4900}=70$.

Step6: Calculate $-\sqrt{\frac{121}{49}}$

Since $(\frac{11}{7})^{2}=\frac{121}{49}$, then $-\sqrt{\frac{121}{49}}=-\frac{11}{7}$.

Step7: Calculate $-\sqrt{25}$

Since $5^{2}=25$, then $-\sqrt{25}=-5$.

Step8: Calculate $\sqrt{0.0036}$

Since $0.06^{2}=0.0036$, then $\sqrt{0.0036}=0.06$.

Step9: Calculate $-\sqrt{\frac{4}{81}}$

Since $(\frac{2}{9})^{2}=\frac{4}{81}$, then $-\sqrt{\frac{4}{81}}=-\frac{2}{9}$.

Step10: Calculate $\sqrt{1}$

Since $1^{2}=1$, then $\sqrt{1}=1$.

Step11: Calculate $-\sqrt{400}$

Since $20^{2}=400$, then $-\sqrt{400}=-20$.

Step12: Calculate $\sqrt{\frac{9}{2500}}$

Since $(\frac{3}{50})^{2}=\frac{9}{2500}$, then $\sqrt{\frac{9}{2500}}=\frac{3}{50}$.

Step13: Calculate $-\sqrt{441}$

Since $21^{2}=441$, then $-\sqrt{441}=-21$.

Step14: Calculate $-\sqrt{1600}$

Since $40^{2}=1600$, then $-\sqrt{1600}=-40$.

Step15: Calculate $\sqrt{0.25}$

Since $0.5^{2}=0.25$, then $\sqrt{0.25}=0.5$.

Step16: Calculate $\sqrt{\frac{16}{900}}$

Since $(\frac{2}{15})^{2}=\frac{16}{900}$, then $\sqrt{\frac{16}{900}}=\frac{2}{15}$.

Answer:

1. $-\sqrt{10000}=- 100$
2. $-\sqrt{\frac{1}{9}}=-\frac{1}{3}$
3. $\sqrt{121} = 11$
4. $\sqrt{4900}=70$
5. $-\sqrt{\frac{121}{49}}=-\frac{11}{7}$
6. $-\sqrt{25}=-5$
7. $\sqrt{0.0036}=0.06$
8. $-\sqrt{\frac{4}{81}}=-\frac{2}{9}$
9. $\sqrt{1}=1$
10. $-\sqrt{400}=-20$
11. $\sqrt{\frac{9}{2500}}=\frac{3}{50}$
12. $-\sqrt{441}=-21$
13. $-\sqrt{1600}=-40$
14. $\sqrt{0.25}=0.5$
15. $\sqrt{\frac{16}{900}}=\frac{2}{15}$