HSN.RN.A.2 Math Practice Questions — Sports Academy Games

Practice playeasy

Which expression is equivalent to $\sqrt{72}+\sqrt{98}$ ?

$\sqrt{72}=\sqrt{36 \cdot 2}=6\sqrt{2}$ and $\sqrt{98}=\sqrt{49 \cdot 2}=7\sqrt{2}$ . Adding like radical terms gives $6\sqrt{2}+7\sqrt{2}=13\sqrt{2}$ .

Practice playeasy

If $\Large a$ and $\Large b$ are positive, which expression is equivalent to $\Large \sqrt[4]{a^8 b^{12}}$ ?

Divide each exponent by $\Large 4$ : $\Large a^{\tfrac{8}{4}} b^{\tfrac{12}{4}} = a^2 b^3$ .

Practice playeasy

The speed, in meters per second, of a certain water wave can be estimated by multiplying the wavelength, in meters, by $12$ and then taking the square root of the product. According to this method, what is the estimated speed, in meters per second, of a wave with a wavelength of $45$ meters?

The product is $45 \cdot 12 = 540$ . Factor $540 = 36 \cdot 15$ , where $36$ is the largest perfect-square factor. So $\sqrt{540} = \sqrt{36 \cdot 15} = 6\sqrt{15}$ , and $15 = 3 \cdot 5$ is square-free.

Practice playeasy

Which expression is equivalent to $\sqrt{720}$ ?

$720 = 144 \cdot 5$ , so $\sqrt{720} = \sqrt{144 \cdot 5} = 12\sqrt{5}$ .

Practice playeasy

Which expression is equivalent to $\sqrt{80}+\sqrt{45}$ ?

$\sqrt{80}=\sqrt{16 \cdot 5}=4\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$ . Adding like radical terms gives $4\sqrt{5}+3\sqrt{5}=7\sqrt{5}$ .

Practice playeasy

If $\Large m$ and $\Large n$ are positive, which expression is equivalent to $\Large \sqrt[5]{m^{10} n^{15}}$ ?

Divide each exponent by $\Large 5$ : $\Large m^{\tfrac{10}{5}} n^{\tfrac{15}{5}} = m^2 n^3$ .

Practice playeasy

The sound intensity level, in a simplified unit, of a certain speaker can be estimated by multiplying the speaker's power, in watts, by $8$ and then taking the square root of the product. According to this method, what is the estimated intensity level of a speaker with a power of $75$ watts?

The product is $75 \cdot 8 = 600$ . Factor $600 = 100 \cdot 6$ , where $100$ is the largest perfect-square factor. So $\sqrt{600} = \sqrt{100 \cdot 6} = 10\sqrt{6}$ , and $6 = 2 \cdot 3$ is square-free.