Question

Pat shows that 16 1/2 = √16. What is one possible way Pat could have shown this correctly?

16\frac{1}{2}=\left(4\cdot4\right)^{\frac{1}{2}}=4^{\frac{1}{2}}\cdot4^{\frac{1}{2}}=4^{\frac{1}{2}}+^{\frac{1}{2}}=4^{1}=4=\sqrt{16}

16\frac{1}{2}=\left(8\cdot8\right)^{\frac{1}{2}}=8^{\frac{1}{2}}\cdot8^{\frac{1}{2}}=8^{\frac{1}{2}}+^{\frac{1}{2}}=8^{1}=8=\sqrt{16}

16\frac{1}{2}=\left(8+8\right)^{\frac{1}{2}}=8^{\frac{1}{2}}\cdot8^{\frac{1}{2}}=8^{\frac{1}{2}}+^{\frac{1}{2}}=8^{1}=8=\sqrt{16}

16\frac{1}{2}=\left(4+4\right)=4^{\frac{1}{2}}\cdot4^{\frac{1}{2}}=4^{\frac{1}{2}}+4^{\frac{1}{2}}=4^{1}=4=\sqrt{16}

16\frac{1}{2}=\left(4\cdot4\right)^{\frac{1}{2}}=4^{\frac{1}{2}}\cdot4^{\frac{1}{2}}=4^{\frac{1}{2}}\cdot^{\frac{1}{2}}=4^{1}=4=\sqrt{16}

Answer 1

[AI-generated answer — Bot GPT 3.5]

One possible way Pat could have shown this correctly is by using the property that the square root of a number multiplied by itself equals the original number. In this case, Pat could have shown that 16 1/2 is equal to (√16)(√16) which is equal to 4 * 4 = 16.