Algebra Class: Surds and Indices

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Questions and Answers

What is the result of multiplying the surds $2 \times 3$?

  • $4$
  • $8$
  • $6$ (correct)
  • $5$

The square root of $25$ simplifies to $5$.

True (A)

What is the simplified form of $\sqrt{200}$?

10\sqrt{2}

$2 + 3\sqrt{5}$ simplifies to _________ when there is another term with $\sqrt{5}$ to add.

<p>5\sqrt{5}</p> Signup and view all the answers

Match the following operations with their results:

<p>$\sqrt{12}$ = $2\sqrt{3}$ $10 \div 2$ = $5$ $\sqrt{45}$ = $3\sqrt{5}$ $\sqrt{16}$ = $4$</p> Signup and view all the answers

What is the result of the operation $3^2 - 8$?

<p>2 (A)</p> Signup and view all the answers

What is the result of dividing the surd $12 \div 6$?

<p>$3$ (A)</p> Signup and view all the answers

What are the results of adding $5 + 3\sqrt{5}$?

<p>5 + 3\sqrt{5}</p> Signup and view all the answers

$4^3 ÷ 2^6$ equals $24^2$.

<p>False (B)</p> Signup and view all the answers

What is the simplified form of $15x^3 ÷ 3x^2$?

<p>5x</p> Signup and view all the answers

Surds can only be simplified if they contain square numbers.

<p>True (A)</p> Signup and view all the answers

The expression $x^{-2}$ can be rewritten in ordinary form as ___.

<p>1/x²</p> Signup and view all the answers

Match the following expressions with their equivalent forms:

<p>x^0 = 1 x^3 = x<em>x</em>x x^-1 = 1/x x^(1/2) = √x</p> Signup and view all the answers

What is the result of the operation $5 imes 5^2$?

<p>125 (B)</p> Signup and view all the answers

The expression $x^2 ÷ x^2$ is equal to 1 for any non-zero x.

<p>True (A)</p> Signup and view all the answers

What is the result of $32 - 48 - 75$?

<p>-91</p> Signup and view all the answers

What is the ordinary form of $x^{1}$?

<p>x (C)</p> Signup and view all the answers

The expression $x^{2}$ is equivalent to $x imes x$ in ordinary form.

<p>True (A)</p> Signup and view all the answers

What is the ordinary form of $x^{ rac{1}{2}}$?

<p>√x</p> Signup and view all the answers

The expression $x^{1/3}$ represents the __________ of x.

<p>cube root</p> Signup and view all the answers

Match the ordinary form expressions with their index form expressions:

<p>1 = A: $x^{0}$ 2 = B: $x^{1}$ 4 = C: $x^{2}$ 8 = D: $x^{3}$</p> Signup and view all the answers

Which of the following is the index form of the expression $x imes x imes x$?

<p>$x^{3}$ (C)</p> Signup and view all the answers

The expression $x^{ rac{1}{4}}$ can be expressed as $x^{4}$ in ordinary form.

<p>False (B)</p> Signup and view all the answers

What is the ordinary form of $x^{2}$?

<p>x squared</p> Signup and view all the answers

The index form of $4$ is __________.

<p>$2^{2}$</p> Signup and view all the answers

Match the following index forms with their ordinary equivalents:

<p>$x^{3}$ = A: $x imes x imes x$ $x^{ rac{1}{2}}$ = B: √x $x^{2}$ = C: $x imes x$ $x^{0}$ = D: 1</p> Signup and view all the answers

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Study Notes

Surds

  • Multiplying surds: Multiplying surds involves multiplying the values inside the radical symbol. For example, 2√3 × √10 = √60.
  • Dividing surds: Dividing surds involves dividing the values inside the radical symbol. For example, √10 ÷ √2 = √5.
  • Simplifying surds: Simplifying surds involves taking out perfect square numbers from inside the radical symbol and finding their root. For example, √4a = √(4 × a) = 2√a.
  • Adding and subtracting surds: Adding and subtracting surds requires the same surd to be present in both terms. For example, √b + 2√b = 3√b.

Indices

  • Multiplying indices: When multiplying indices with the same base, add the exponents. For example, x * x = x².
  • Dividing indices: When dividing indices with the same base, subtract the exponents. For example, x ÷ x = x⁻¹.
  • Powers of indices: When raising a power to another power, multiply the exponents. For example, (x²)³ = x⁶.
  • Negative indices: A negative index represents the reciprocal of the base raised to the positive value of the index. For example, x⁻¹ = 1/x.
  • Fractional indices: A fractional index indicates taking the root of the base. For example, x½ = √x.
  • Power of zero: Any base raised to the power of zero is equal to one. For example, x⁰ = 1.

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