H0rnyPhlipinesidn
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calculate √17+4
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︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎√17-4


with solution po, thanks​

Sagot :

TheFixeridn

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Answer: [tex]\boxed{\sf{33 + 8\sqrt{17}}}[/tex]

SOLUTION:

» The number 1 is the neutral multiplication factor, so we can write that:

  • [tex]\sf 1 = \frac{\sqrt{17}+4}{\sqrt{17}-4}[/tex]

» Multiply expression above by the given number.

  • [tex]\sf \frac{\sqrt{17}+4}{\sqrt{17}-4} \times 1 = \frac{\sqrt{17}+4}{\sqrt{17}-4} \times \frac{\sqrt{17}+4}{\sqrt{17}+4} =[/tex]

  • [tex]\sf \frac{(\sqrt{17}+4) \times (\sqrt{17}+4)}{(\sqrt{17}-4) \times (\sqrt{17}+4}[/tex]

» We will use the short multiplication formula:

  • [tex]\sf (a - b)(a + b) = a^2 - b^2[/tex]

» When we multiply the given number by 1, we can use the short multiplication formula in the fraction's denominator.

  • [tex]\sf \frac{(\sqrt{17}+4) \times (\sqrt{17}+4)}{(\blue{\sqrt{17}-4}) \blue{\times} (\blue{\sqrt{17}+4})}[/tex]

  • [tex] = \frac{(\sqrt{17}+4)^2}{(\sqrt{17})^2 - (4)^2}[/tex]

  • [tex]\sf = \frac{(\sqrt{17}+4)^2}{17 - 16}[/tex]

  • [tex]\sf = \frac{(\sqrt{17}+4)^2}{1}[/tex]

  • [tex]\sf = (\sqrt{17}+4)^2[/tex]

» Now you can find the result:

  • [tex]\sf (\sqrt{17}+4)^2 = 17 + 8\sqrt{17} + 16 = [/tex]

  • [tex]\sf 33 + 8\sqrt{17}[/tex]

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