In my textbook, one of the examples of a heterogeneous mixture is milkshake, I don't see how ? I think the answer depends on the fact that How many phases are there in a milkshake, which I think should be only 1 (if we don't consider any "added stuffs":)
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It depends on the scale. Milk is homogeneous when observed with our naked eyes. It becomes heterogeneous under the microscope. – Maurice Jan 26 '23 at 13:48
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3Rule of thumb: If a solution is not transparent, it is most probably a heterogeneous solution such as milk (colloidal). Thus, milkshake is definitely a heterogeneous mixture. – Mathew Mahindaratne Jan 26 '23 at 15:56
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For a consumer, the milkshake is heterogeneous, as there are seen air bubbles and eventually small pieces of fruit. Fresh milk would be homogeneous for him. For a scientist with a microscope, both would be heterogeneous. For across the street observer with a binocular, both would be homogeneous. – Poutnik Jan 26 '23 at 17:02
3 Answers
Yes, a milkshake is heterogeneous.
milk is heterogeneous all on its own; fat globules in the milk are a different phase than water solutions in the milk. (Curds vs. whey).
ice cream adds two additional heterogeneities: it contains microscopic ice crystals, and ice is a different phase than both water and fat globules. It also contains tiny air bubbles, and this is a fourth phase.

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Homogenity/heterogenity is dependent on evaluation conditions.
A mixtures is heterogenous if both these conditions are true:
- Local variability of mixture properties are above the threshold of
- property value resolution AND
- mixture application requirement.
- Spacial granularity of the above variability is above the threshold of
- spacial resolution AND
- mixture application requirement.
Otherwise, a mixture is homogenous.
If values vary less than we notice or care
OR if values vary within smaller distance than we notice or care
THEN the mixture is homogenous.
Every mixture can be considered homogenous or heterogenous at certain ( sometime extreme) conditions.
- If there are floating evenly distributed potatoes in water, observed by a telescope with resolution $\pu{1 m}$, it is homogenous mixture.
- If there is an old favourite red T-shirt, a "16-Windows(3.x)-colors man" may say it is still homogenously colored, even if his wife disagrees.

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Milk is a colloid dispersion, i.e. a
"substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance."
(source: English Wikipedia)
As such, visible light is scattered when it passes this medium; equally known as Tyndall effect. In case you get your hands on a bright light source, you then can monitor the optical path across this medium. It needn't be a laser as in this video recording about a very dilute milk:
(screen photo of the mentioned video, 1:28 min into the recording)
Addition after a comment:
Replication with «true milk» requires a brilliant light source passing an aperture narrow enough. On the other hand, because of the high concentration of particles with a dimension about light's wavelength, scattering occurs so frequently that the beam fuzzes out rapidly: (For these two transmission mode observations, equally note color of the milk and glare (and apparent color) of the glass in the second run with milk which is less prominent for the experiment with tap water in the experiment.)
Setup: daylight-white light of a LED torch (focus to infinity) passes a flat bottom glass, perpendicular to the surface (aperture: $\pu{3 mm}$ diameter, thickness glass wall: $\approx \pu{2 mm}$). Path length $\approx \pu{10 mm}$ for either water (first experiment), or fresh milk (second experiment; 1.5% fat, purchased less than $\pu{12 h}$ earlier, which passed both Pasteurization and homogenization. Homogeneous hereby is not about a discern between solution (e.g., $\ce{NaCl}$ dissolved in water), or collide (e.g., fat dispersed in milk), but refers to a narrowed (i.e., adjusted) particle size distribution of the fat globules suspended in milk after passing homogenization for which Wikipedia reports
an average diameter of two to four micrometers [of unhomogenized cow's milk] and with homogenization, [an] average [of] around 0.4 micrometers.
($\pu{1 µm} = 1 \times \pu{10^-6 m}$, and $\pu{1 nm} = 1 \times \pu{10^-9 m}$; so $\pu{0.4 µm} \approx \pu{400 nm}$. For comparison: average diameter of a human hair $\approx \pu{100 µm}$ (ref), wavelength of visible light $\approx 250\ldots\pu{700 nm}$.)

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Hmm, but if the Tyndall effect occurs in the diluted milk the same observed way in every place, with liquid not manifesting spatial variations of it ... we have homogeneous liquid in Tyndall effect measurement context. If it varied e.g. due fat separation, it would be in the given context heterogenous. – Poutnik Jan 26 '23 at 18:35
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@Poutnik If there is no agreement / convention / definition about homogenous / heterogenous (which may vary over time, perspective / community) the same word may refer to different qualities. This is why your comment prompted an experiment to extend the answer. – Buttonwood Jan 26 '23 at 21:03
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1There are procedural conventions in some particular cases, but generally, homogenity as having uniform properties depends on how thoroughly and zoomed in/out we look. Evaluating dough, a baker and a food scientist would have very different criteria for homogenity. – Poutnik Jan 27 '23 at 07:15