Simplify. sqrt((2-sqrt3)sqrt(7+4sqrt3))

Use Property of Square Roots: We are given the expression sqrt((2-sqrt(3)) * sqrt(7+4sqrt(3))). To simplify this, we can use the property of square roots that states sqrt(a) * sqrt(b) = sqrt(a * b).Multiply Quantities: Now, let's multiply the two quantities inside the square roots together. (2 - sqrt(3)) * (7 + 4sqrt(3)) = 2*7 + 2*4sqrt(3) - sqrt(3)*7 - sqrt(3)*4sqrt(3)Perform Multiplications: Perform the multiplications. 14 + 8sqrt(3) - 7sqrt(3) - 4*3Combine Like Terms: Combine like terms and simplify. 14 + 8sqrt(3) - 7sqrt(3) - 12 = 14 - 12 + 8sqrt(3) - 7sqrt(3)Further Simplification: Further simplification gives us: 2 + sqrt(3)Take Square Root: Now we take the square root of the simplified expression. sqrt(2 + sqrt(3))

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Algebra 1

Multiply radical expressions

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Q. Simplify.

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\sqrt{(2-\sqrt{3}) \sqrt{7+4 \sqrt{3}}}

Use Property of Square Roots: We are given the expression $\sqrt{(2-\sqrt{3}) \cdot \sqrt{7+4\sqrt{3}}}$ . To simplify this, we can use the property of square roots that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ .
Multiply Quantities: Now, let's multiply the two quantities inside the square roots together. $\newline$ $(2 - \sqrt{3}) \times (7 + 4\sqrt{3}) = 2\times7 + 2\times4\sqrt{3} - \sqrt{3}\times7 - \sqrt{3}\times4\sqrt{3}$
Perform Multiplications: Perform the multiplications. $14 + 8\sqrt{3} - 7\sqrt{3} - 4\times 3$
Combine Like Terms: Combine like terms and simplify. $14 + 8\sqrt{3} - 7\sqrt{3} - 12 = 14 - 12 + 8\sqrt{3} - 7\sqrt{3}$
Further Simplification: Further simplification gives us: $2 + \sqrt{3}$
Take Square Root: Now we take the square root of the simplified expression. $\sqrt{2 + \sqrt{3}}$