Question

ChallengE
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Answer 1

Question

• Simplify:

`\displaystyle{\sf\:4\:√(48)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)}`

Answer :

`\displaystyle{\boxed{\red{\sf\:4\:√(48)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)\:=\:(127\:√(3))/(6)}}}`

Step-by-step-explanation:

We have given an expression.

We have to simplify the expression.

The given expression is

`\displaystyle{\sf\:4\:√(48)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:4\:√(16\:*\:3)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)}`

We know that,

`\displaystyle{\boxed{\pink{\sf\:√(a\:*\:b)\:=\:√(a)\:*\:√(b)\:}}\:\cdots\sf\:a\:,\:b\:\geq\:0}`

`\displaystyle{\implies\sf\:4\:√(16)\:*\:√(3)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:4\:*\:4\:√(3)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)}`

We know that,

`\displaystyle{\boxed{\blue{\sf\:\sqrt{(a)/(b)}\:=\:(√(a))/(√(b))\:}}\:\cdots\sf\:b\: > \:0}`

`\displaystyle{\implies\sf\:16\:√(3)\:-\:(5)/(2)\:*\:(√(1))/(√(3))\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:16\:√(3)\:-\:(5)/(2)\:*\:(1)/(√(3))\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:(16\:√(3)\:*\:2\:√(3)\:-\:5)/(2\:√(3))\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:(16\:*\:2\:√(3)\:*\:√(3)\:-\:5)/(2\:√(3))\:+\:6\:√(3)} \\ \\\displaystyle{\implies\sf\:(32\:*\:3\:-\:5)/(2\:√(3))\:+\:6\:√(3)}`

`\displaystyle{\implies\sf\:(8\:*\:4\:*\:3\:-\:5\:+\:(\:6\:√(3)\:*\:2\:√(3)\:))/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(8\:*\:12\:-\:5\:+\:(\:6\:*\:2\:*\:√(3)\:*\:√(3)\:))/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(8\:*\:12\:-\:5\:+\:(\:12\:*\:3\:))/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(8\:*\:12\:-\:5\:+\:12\:*\:3)/(2\:√(3))} \\ \\ \\ \displaystyle{\implies\sf\:(8\:*\:12\:+\:12\:*\:3\:-\:5)/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(12\:(\:8\:+\:3\:)\:-\:5)/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(12\:*\:11\:-\:5)/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(132\:-\:5)/(2\:√(3))} \\ \\ \\\displaystyle{\implies\sf\:(127)/(2\:√(3))} \\ \\ \\ \displaystyle{\implies\sf\:(127)/(2\:√(3))\:*\:(√(3))/(√(3))} \\ \\ \\\displaystyle{\implies\sf\:(127\:√(3))/(2\:*\:3)} \\ \\ \\\displaystyle{\implies\sf\:(127\:√(3))/(6)} \\ \\ \\ \displaystyle{\therefore\:\underline{\boxed{\red{\sf\:4\:√(48)\:-\:(5)/(2)\:\sqrt{(1)/(3)}\:+\:6\:√(3)\:=\:(127\:√(3))/(6)}}}}`