3 years ago

Simplify: √ (50x^7y^6)

1 answer:

5 0

$\sqrt{50x^7y^6} = 50^{\frac{1}{2}} (x^7)^{\frac{1}{2}} (y^6)^{\frac{1}{2}} = 50^{\frac{1}{2}}x^3 x^{\frac{1}{2}}y^3 = 5(2)^{\frac{1}{2}}x^3x^{\frac{1}{2}}y^3$

$5(2)^{\frac{1}{2}}x^3x^{\frac{1}{2}}y^3 = 5x^3y^3 \sqrt{2x}$

Your answer is $5x^3y^3 \sqrt{2x}$

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Write the following quotient in the form a+bi.<br> -7i/2-7i

Helga [31]

Answer:

$\large\boxed{\dfrac{49}{53}-\dfrac{14}{53}i}$

Step-by-step explanation:

$\text{Use}\\\\i=\sqrt{-1}\to i^2=-1\\\\(a-b)(a+b)=a^2-b^2\to(a-bi)(a+bi)=a^2+b^2\\\\\text{distributive property}\ a(b+c)=ab+ac\\---------------------\\\\\dfrac{-7i}{2-7i}=\dfrac{-7i}{2-7i}\cdot\dfrac{2+7i}{2+7i}=\dfrac{-7i(2+7i)}{2^2+7^2}=\dfrac{(-7i)(2)+(-7i)(7i)}{4+49}\\\\=\dfrac{-14i-49i^2}{53}=\dfrac{-14i-49(-1)}{53}=\dfrac{-14i+49}{53}\\\\=\dfrac{49}{53}-\dfrac{14}{53}i$